Can you help me in my search for my first turntable?

Another vote for the Rega RP10 !  Do it once and do it right....

Are you sure you are just now getting into vinyl??

I recall you from other threads.............

Why not check out the Rega RP10 if you have not already?
I am assuming you are in living in the Royal playground as you are talking
in the UK's bees and homey...................
https://shop.grahams.co.uk/collections/turntables-vynl/products/rega-rp10

I wouldn’t get hung up on if a table is sprung or not. It boils down to the sound you prefer between the options. They have distinct differences and NO ONE can tell you what you like. That’s a recipe for someone else’s cake , that you put up the cake to buy . Listen to the difference yourself and now that you have heard a couple decent sprung tables , see if you can hear a non suspended belt and a non suspended direct drive. Your post though, in your 6 thousand quid budget lacks a crucial part as often these posts do. The Phono pre . If it isn’t up to task , you won’t really know how good/bad for your wants that table/arm/cart will/could be.
I have a suspended / belt drive (Orbe SE) and a non suspended belt drive (Micro 5000).
I like what both do and there differences. I don’t do direct drive anymore as I don’t
find it as natural sounding as I once thought, (IMHO, and that could be a change in my hearing) but the dynamic drive of them can sure be fun. The older Garrard tables brought up to new spec can be quite good. Try to hear one if you can. You may overcome the looks after you hear one that’s well set up.
Others will completely 180 my view and feel the direct drive is the only way to go. That’s fine, I get it , but what matters is YOUR opinion and 6000 quid will get you a long way down the road. Just make sure its the road you want to be on. They all have their pitfalls and strengths in sound and set up. And don’t make the phono pre an after thought, it needs to be able to match your cartridge choice(s) if your pre amp can’t to have success. You may want to also consider
how much cost , access and size of a record collection your first turntable will lead to. Good clean reasonable sized selection of records is the only way to enjoy a good vinyl rig, obviously.      Good Luck.

Thanks for the advice on VTA. Definitely something that never occurred to me. Can I just ask, why do you recommend a table with no or little spring? Could you make a recommendation on a table or two? Thanks

Look for a turntable that has a tonearm with a VTA micrometer that permits you to adjust the VTA while the record is playing, and don't settle for anything less, or you will be sorry. Some of the tonearms that allow this are VPI Memorial arm, Graham and Triplaner.  Myself, I recommend  a heavy table, with either none or very little spring.

My next table will be the new Technics 1200G. 

Just waiting for a deal!

The new red and black SME look really nice too but I haven't heard one.

The best turntable in your price range would be the SME Model 15. I honestly can't think of anything better. I own a Gyro SE with an SME 309 tonearm and it's also fantastic. But my next table will be either SME 10 or 15. 

Check out SME!

Get a restored Garrard 301 with a custom plinth and a Fidelity Research FR64S tonearm! Add a Miyajima Shilabe mc cartridge and you will have a world-class TT system!

Apologies, £6000!