Sorry for your difficult situation, OP.
You have some options.
As PP have said, yep, you can buy outright.
However, even though you are a low earner, the fact that you have such a significant down payment would probably enable you to be able to take out a mortgage on top, if you could afford to put your current rent into a mortgage for somewhere bigger. Because with a large amount of equity (the ‘paid for’ amount as opposed to the amount borrowed from the mortgage lender) the lenders see you as less of a risk.
So you could talk to a mortgage advisor, but be aware that in the end the choice is yours and not to get dazzled!
So, if the your inheritance could buy you a 1 bed flat, you might be able to get a small mortgage on top and buy a 2 bed.
Remember as an owner occupier you need to keep savings or budget for for a new boiler, roof repairs, etc. Saving what you currently pay in rent could go towards a house maintenance pot.
Rough Budget for buying;
Survey £600
Solicitors plus their costs (they will pay for searches etc): £2-3k
Stamp duty if your property is over £300k
As you are a first time buyer My advice would be use a proper solicitor not a cheap online ‘conveyancer’.
And keep asking questions on this board 