OK, thanks for the clarification. The Sky router is doing its job, so a "better" Sky router would not offer any improvement in terms of signal speed.
Now, we need to talk about wireless signal strength. If you want to leave the Time Capsule where it is currently located, there are two basic methods that would deliver greater signal strength to the lounge area.
Method 1......Best performance......Add an AirPort Express in the lounge area (preferably where it will have line-of-sight with the wireless devices that you will use in the lounge area. Connect an Ethernet cable from the AirPort Express back to the Time Capsule. With this setup, you could expect about equal wireless performance and speed as you have now when you are in the study.
Next Best Performance......if you cannot run the Ethernet cable between the Time Capsule location and AirPort Express in the study, use a pair of HomePlug adapters to send the Ethernet signal in that manner. IF.....the Home Plug adapters will deliver 8-9 Mbps speeds to the AirPort Express, then the AirPort Express performance will be quite close to the performance of using an Ethernet cable.
Method 2......Significant Compromise Performance......If you cannot run the Ethernet cable or use Home Plug adapters to send a signal to the AirPort Express, then, the Express does have the capability of receiving a wireless signal and "extending" or "repeating" it toward the lounge area. To do this, the Express would need to be located about half way between the Time Capsule and the lounge area. This type of method will deliver more wireless signal strength to the lounge area.....but.....and this is a big BUT......there will be a signal speed loss of at least half when you use this method. So the best performance that you could hope to achieve would be a signal that is both weaker and slower in the lounge area that it is now near the study.
There will be an improvement in the signal quality in the lounge area, so Method 2 might be good enough to accomplish your goal of a better signal quality in the lounge area. But, you will not know how well this method might work....or IF it might work.....until you try it out in your home.
Now, it is up to you to decide if you want to proceed and how you want to proceed.