Based on your other thread, you'll be looking to rent a modern 4 seater around the London area. You will be lucky to get 12 hours for £2k a year and maybe 15-18 hours a year for £3k - and that excludes extras such as membership fee, landing fees, medical, instructor flights for revalidation or if out of club currency.
You probably need to think about downsizing from a PA28/C172 if you're wanting to get more hours for £3k. Or look at buying a share in an LAA aircraft, but that would mean an initial outlay. Or move up north, where hourly rental can be 25% cheaper than London!