Welcome!
You will get a lot of advice on here, from folk with experience in a lot of fields. Some of it may even conflict!
Despite being in purdah under current conditions, I would advise two things.
1 ) Join the I o W Model Engineering Society
2 ) Be patient, and do nothing until things improve.
If you are a complete newbie, you need basic knowledge and face to face advice to get some experience before embarking on a model. You will scrap fewer expensive parts that way, and lessen the risk of becoming disillusioned..
Better to scrap a bit of bar used as a test / learning piece, than a casting as part of a kit.
A 20mm bar can be used to learn turning or facing by reducing it to 19 mm and then to 18 mm, and so on to gain experience, if only of acquiring the ability to turn a traverse handle at a reasonably steady speed. And the effect of various speeds and feeds.
You will begin to gather that you need tools, drill chucks an drills to start work.
The budget will control what machines you buy, and again, you need advice, especially if contemplating any secondhand machine. For that, you definitely need someone experienced to come with you to check the prospective purchase.. Also, a sympathetic Club member can give you face to face tuition and demonstrations.
In the meantime, devote some of the budget to buying a few books, to increase your understanding.
My suggestions would be:
L H Sparey "The Amateur's Lathe"
Ian Bradley "The Amateur's Workshop"
Tubal ,Cain "The Model Engineer's Handbook" This is a most useful reference book.
These will take £25 – 30 out of the budget, but may pay for themselves by a better understanding of what is going on, and avoiding damage to tool, machine, and possibly you!
Reading will not make you an expert, but give an understanding, so that you can avoid some of the total newbie's mistakes.
Before very long you will find that a set of Zeus charts are very useful.
A cheap start for measuring instruments would be a digital Calliper. You can get cheap ones for not much more than £10 from LIDL or ALDI when they come on special offer.
If you want to jump in straight away, for about £25 you could buy a Moore and Wright one from Machine DRO, which may be less expensive in batteries, in the long run, and better quality..
As an Apprentice, I found that putting on a 0.010" cut reduced diameter by 0.020", as a surprising first lesson, and later that the milling machine cut far better when I changed it to rotate in the right direction!
Ultimately, you will gain a lot of pleasure and satisfaction from Model Engineering, but learning to walk comes before running or sprinting.
Hope this helps a little.
Howard