"Little overlap" but there
is an overlap at the top end of OP's budget, therefore RTX v GTX is an issue, especially if one can source a good deal.
It is essential you specify
exactly what you want from this laptop & your priorities - how long before you replace it, graphics settings & res requirements, which games you play, desired VR compatibility etc. Additionally, whether compromises would be acceptable on those criteria if you save money. If you can provide this info, helping you pick a laptop to meet your needs will be
much easier.
For basic playability a 1050ti is perfectly viable at high settings which on a 15.6" screen is fine but I'd agree with Morbad generally that scaling up is desirable & the 1660ti is a good card in terms of bang for buck; if you can stretch to £1200 or so & a 2060, all the better for the architecture advantages. I would add that 16GB RAM is the new benchmark by general consensus going forward in games development.
I generally replace my rig & laptop Evey 2/3 yrs & I have bought 5 laptops in the last 6 months - not all for myself!

I've just bought an Asus Rog Strix with a 2070 on behalf of my brother for £300 over your budget limit (he's now my slave until he pays off the balance...ahh good times ahead for this tyrant!) It's an absolute beast of a laptop for a little over what I paid for my Msi 1060, a year ago - grrrr!; if you can find the extra I'd glad to give you the link when I get home later. (On my phone right now!)
& great news...one can type "crap" without the swear-filter kicking in..
crap,crap,crap...see?