Is there a particular reason/occasion for the gift, OP? If not, I'd ask my parents to hold onto it in their own funds for now, with the expectation that they'd be able to gift it to you when you're in a better position to use it effectively and efficiently. It's not a sensible gift when it's going to have such a big impact on your income without actually providing much in the way of material benefit.
Even if you're of the mind that family should help family get off of benefits (not my style, but some people's), it's still a short gain for a long-term loss. In a few years, you'll be able to work full time, get a reasonable mortgage, and with luck use the deposit to get off benefits for the long term. If you get it now, it will merely give a short-term reduction in benefits without providing a means to get off them in the longterm. Again, I don't think this is particularly material, but if you're hearing about this from others, this is a reasonable answer.
Alternately, if you're comfortable with it and could make a sizable salary with your current qualifications, you could ask your parents to pay for childcare while you get back to work full-time. You can get back on the career ladder, with the hope of building up your salary by the time your kids are no longer in childcare, and there might be money left to help with a deposit.
But no, I don't think the lump sum cheque is a good plan at the moment.