Hi OP
This is totally counter to my normal instinct. I am 35 and have bought and sold continually since my early twenties. But reading your post and the resulting advice, I'd say the issue is your mum sounds like she is thinking a lot about the generous gift and less about your career, and your success at this placement in particular, which is what will keep all the other plates spinning. If she's worried prices are climbing (depends where and what) and her cash is devaluing in the bank, there are things she can do herself to address that (which given that she managed to amass that sum in the first place she must be aware of) in the short to medium term.
Moving to London and starting a demanding career is enough at once, especially at twenty-three. I trained as a lawyer, with a long commute, as I was very 'practical', and I began to regret it quite quickly, as it was grim. I don't mind a commute now, but I'm married with kids and don't want to stay out til 4am dancing anymore.
It will take you time to organise a mortgage, view properties and scope out your prospects at your firm. A year of rent is money you'll never recover but there is nothing worse than feeling pressured in your life choices, and if you don't really have to be, then why?
Unless you have a very clear idea of where you want to live, and are prepared to put up with the risk of feeling life is going on elsewhere, you won't lose much by holding off. If it's now or never, take the money, of course, but I can't see how you can buy without renting for six months or so first without taking a huge risk.
Also does your mum know most grad schemes expect ridiculous flexibility and you could miss out on opportunities by being tied? If you do buy, try to ensure you can rent easily /offload quickly if you need to.
It's not ungrateful to want to get something right, it's all in the way you phrase it to your mum.
Good luck!!