Nick, I do not have nor have I ever had any Beta products installed on any of my Apple devices or for that matter my Microsoft PCs. I strongly advise against it unless the person is a developer. We are not allowed to discuss Betas here anyway.
Regarding a new router, my 2 cents… wait a bit before you buy one. Then again here in the US I could buy one at the Apple Store and return it within 14 days, don't know if the same policy applies in the UK, likely yes. I would try this myself but I have a more complicated networking system at home than what I have discussed here so far and Apple’s Airports will not let me do what I want. Apple is well known for making things simple at the expense of user control. I have multiple APs and my AT&T / Cisco system allows me great flexibility throughout my home.
A recent poster on another thread had similar issues a couple of weeks back, had an old Airport which he did not mind replacing as it was getting "arthritic", bought a new Express (not an Extreme) and it worked for him. There is no guarantee for you of course but assuming that your 6 does not have a hardware defect, I would give it a 75%+ chance that it will work. Going Apple to Apple greatly enhances compatibility.
The issue at hand is simply the “iOS radio hardware/software accessing the router and maintaining a stable connection” and while mDNSResponder in iOS 7 worked well (not perfect) with just about any up-to-date, WI-FI certified router (as it should), DiscoveryD does not. Apple attempted to fix DiscoveryD without success (at least so far) and thus reverted back to mDNSR with OS X 10.10.4.
Regarding the complicated topic of why some devices work and some don’t with the same router - and why some work in various places and not others - without getting too technical here, there is a general misconception that all iPhone 6 (how do I say sixes, not 6s as there is no such thing) should behave the same, barring defective hardware/software. Yes ones and zeros are just that but how they interact with the hardware is another matter. The answer generally lies with manufacturing "tolerances", i.e., no 2 iPhone 6 (I'll skip the s) are ever the same, no 2 Airport Extremes are ever the same, no 2 car pistons are ever the same.... They may meet tolerances and specs established by the manufacturer for wifi radios, displays, chips, etc. but the ones and zeros will behave ever so slightly different in one versus the other. The same applies to 3rd party routers, no two Cisco xxx are ever the same either, and pairing the tolerances of a phone with the tolerances of the 3rd party router adds to the complexity. The routers may be Wi-Fi certified, meet specs, and have up-to-date firmware but they will vary router to router.
As I mentioned before, I have spent around 8 hours on the phone (or maybe more) with various AppleCare reps starting in Dec 2014. I initiated the first call. The original call was escalated to Level 2 after about half an hour with Level 1 (a waste of time that one has to go through to get to 2 but Level 1 solves a lot of simple issues). Level 2 could not resolve the issue of course. My phone and router settings were all verified by a very knowledgeable tech, Bob K. (which I now have on speed dial as he gave me his direct number after hours of effort). Bob "remoted" in to my PC while my phone was connected to iTunes, spent considerable time looking at all he could, but to no avail, then arranged for me to get a new phone at the Apple Store courtesy of Apple, even though mine a 5, was out of warranty already (I must say that Apple has great customer support, way beyond what they are obligated to do). Bob then escalated the case to the Engineering/Development team.
My original phone was in pristine condition but the exchange resulted in a new phone with a new battery, my payoff for the effort. As an aside, the replacement phone lasted one day only. Picked it up one evening at the Genius bar, was told that the phone was brand new because Apple does not replace defective phones with refurbished ones (kudos to Apple). Regardless, the next day the display developed large vertical bars, went back to Genius, they played with it a bit and gave me iPhone #3 which I now have….
In late January I received a call initiated by AppleCare as a result of my posts here and asking to take logs and other info from my devices. AC then tried to set up a conference call with an engineer, the tech, and myself at a given time in late January. I could not make that timeframe as I was headed to a sunny blue water climate for two weeks and thus got dropped - likely some other chap got moved into the queue instead and I did not hear from this tech again. In March I received another call from a different tech, based on my posts here again, and asking for the same information, logs and details from all my devices. No offer was made to patch me to Engineering at that time. Neither of these two techs could hold a candle to Bob.
In your last post you stated “Next port of call is a clean restore with no iCloud backup. Although this will take me hours to get back to how I am now I will try over the weekend.”
Here is a suggestion for you for what ever it is worth. Before you do anything further, connect your 6 to whatever computer you use for syncing. Then do a backup to the computer through iTunes (the default dot will be on iCloud so make sure you change it to computer). Make sure you can then see the time stamp of your last computer backup on iTunes. Then disconnect from the computer and do a backup to iCloud, that way you have both. Now go to your phone itself (with either a 100% charge or better yet, plugged in). Settings > General > Reset > Erase All Content and Settings, and let it rip. When prompted select Set Up As New (and not from iCloud backup). At that time you will have a brand new phone (well almost) assuming the hardware is not defective. Then do the minimal setup necessary to simply allow you to get to Wi-Fi. Then test away and see. One of two results should ensue.
Result #1. Your phone now works well with your Wi-Fi. Bingo! Two choices now, continue setting everything from scratch which depending on what you have could take you many hours - it would me. Second choice, go back to your computer, restore the backup there (more reliable than the iCloud backup) and test again. If it still works you have saved yourself many hours of work. If it does not, you have a corrupted backup because the phone as previously set up had a corrupted configuration or app. Your only choice now is to repeat the Erase All and set up as new all he way.
Result #2. Your phone does not work well with Wi-Fi even after the Erase All and even when set up as New. You either have a defective phone OR we are back at square one with the decision regarding an Airport Extreme and/or waiting for iOS 9. At that point if it was me I would restore the iTunes backup and wait for 9 as I do not want to replace my AT&T / Cisco setup. If you, however, have a 14 day trial option on the Extreme you have a decision to make. Looks like no trip on the Eurostar for you this weekend.
Cheerio,
Carlos (my real name instead of the screen elcpu)