Thanks for your replies.
I have already enabled the Finder to show extensions but they don't work on my Time Machine external hard drive for some reason which I cannot discover.
I did do more research - not sure exactly who these people are but they seem to be involved in the beta testing of Catalina or their own version of it. https://forums.whirlpool.net.au/archive/98mz6153 If you search the page for 'sparse' and the first mention you get is this
'Catalina TM has now overwritten my existing backup and renamed it. File seems to be there, whole 274gb of it, just can't go back in time to restore.
Installed Catalina on an old Mac lappy – Could see the SMB share on install and do a full restore and access SMB shares.
Installed Catalina on new Mac lappy – Bypassed full TM restore on install. Get to desktop, TM SMB share works a treat. Dunno what happened first time I installed.
Load TM up, select the disk/share to restore from, then I saw the sparsebundle file disappear and a new one pop up with a new name... However, the disk is still showing 274gb of used space.
Can I access the old sparsebundle image?'
There's a lot of stuff there but you have to trawl through it if you want the whole story.
What happened in my case was. After the upgrade I was copying some files to a USB hard drive as I only run the Time Machine when I have made a large change. I left it running and went to bed. In the morning the computer had crashed (apparently this is a thing with Catalina), the usb drive was fried and all the files lost.
I backed up my machine to Time Machine twice - it failed once and the second time the data file appeared but the disk drive wouldn't disconnect. I assumed it was Spotlight but it wouldn't disconnect after having the whole night running. I had to force quit.
I had been using iPhotos and having tried Photos once and found it cost me loads of money in data charges with it synching with my phone I decided I didn't like it but there was one photo left in it and so it didn't offer the automatic migration of my photos from iPhoto. I checked how to do this and did it. For a day they were all there and it was fine but when I started up my computer the next day everything after 2017 had gone. Apple Support just kept me on the phone for hours and skirted around the main issue. After various other issues I decided to revert to Mojave and restore from my TM. The install crashed in the first few minutes. The data was still on the drive and was insufficient to allow another install (though it had been a few moments earlier) but the start up disk was gone. First aid did not restore it. I could not access any of it. Apple Support could not help. I erased the disk. It wouldn't let me install from my Time Machine back up. It would only allow another Catalina install. When I tried to migrate the information from my backup during start up it couldn't do it. Apple said all I could do was start afresh and manually copy and paste files from the back up. After some more hours on the phone they decided that the Time Machine back up of my Bookmark.plist was not included in the Time Machine backup and all of that data is lost. They blamed my hard drive. I blame the program which fried my usb and probably had a similar effect on the external hard drive. It seemed to me that this change in back up name may be responsible for the loss of that data and as I'm prepared to risk a backup which is already less than useless and which Apple say I will have to blow away anyway to ensure the disk is working properly, I'm going to give it a go with the help of the script which dot.com kindly provided.
So a warning. Do not leave disk drives attached when you don't have to. Don't try and revert to Mojave - you can only do it after erasing and even then there is a possibility it won't work - it didn't with mine. Be very sure before you start that you have all the data secure and not buried in TM where you can't tell if it is there or not. I'm seriously considering doing manual Backups. OS you can download - why do you need a back up?