Sorry for your loss.
Definitely worth talking to a broker, there are mortgage products available for less than perfect credit ratings and often the interest rate isn't much higher than for standard products, especially as you will have a very good deposit.
You mention that the mortgage will be much less than the rent you're used to paying. That could mean that you could qualify for a larger mortgage, depending on your income, which will allow you to buy a more expensive house, giving you more choice of area and/or property size.
Have a look at the MSE FTB guide, to read up on the process, about fees etc and what to expect as you go through the process.
www.moneysavingexpert.com/mortgages/mortgage-guide/
The other thing to do is to make the money work for you and be safe until you're ready to buy. You don't want to invest it as you can't expose yourself to the risks of the stock market, but you can earn a little interest while you're waiting to buy. You should also be aware that, in the very unlikely event that your bank goes bust, only £85k is protected. Therefore you shouldn't keep more than that amount in any single bank.
Maybe have a look for the best instant access account, you should be able to get 0.6% or so, and maybe if you won't be buying for a few months, put £50k in premium bonds, as you might get prizes worth more than the interest in a normal account.