Hey there

I'm also in the UK and have recently done a big pick review thread which you can find
Here.
In terms of your situation, it does depend on budget to a degree, and whether you want to buy a pre-made set or build your own with individual picks. Personally I think the Southord C2010 is an excellent starter-to-intermediate set. The Southord Max series ending in B (M2000B, M3000B and M4000B) are also great sets to fit a UK profile.
Unfortunately I have little experience of individual picks so you'll have to get others' advice for that. But yeah, depending on whether you want plastic handles and are prepared to pay a little more, both the Southord C2010 and Southord Max series are great picks

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I have tested the Peterson Euro Slenders kit too - and those picks are great, but bear in mind that that particular kit is "Just picks" and doesn't come with a case or tension wrenches, so make sure you pick some wrenches up at least, if you're buying Peterson Euro profile picks.