You are in the same boat as everyone else - if your annual income exceeds the 45k - you will pay the 40% tax on the extra income - as you say if you lose benefits too and have to pay for some liability insurance and it costs you to get to work - that doesn't seem a very attractive option - but hey ho i would go with whatever suits your personal wellbeing first - unless the numbers mean you will be struggling financially. You are pretty unlucky timing wise though to be stuck in the benefits trap and higher rate tax trap at the same time - that normally takes some doing.
There is some light at the end of the tunnel though so lets try and get some good news into play and turn your earnings into tax free cash.
First up there is the new £1,000 trading allowance - that means you can commence as sole trader and if your income is less than £1,000 then the income is tax free. If your income is over £1,000 you can deduct £1,000 from your income providing you claim no other expenses. Tax year ends 5/4/2019 so potentially this could slot in quite nicely if you only take the work part time. Worth checking the benefits side of things to see if you can do some work without being screwed in that regard.
You also have the option of using the cash basis which means you get taxed when paid - so potentially if you bill monthly at the end of the month and get paid 7 days after that then your March income would be paid 7th April and taxed next tax year when presumably higher rate tax won't be an issue. If you did 1k of work in March and stopped 6/4/19 with o further work that 1k could be covered by the trading allowance the following year
So potentially 2k income from now to 5/4/2019 - if 1k was paid after 5/4/19 - the other 1k is covered by the trading allowance so you have zero income for tax purposes. Note you would have to check with benefits bods as to whether they ignore income covered by the trading allowance.
You do also have the ability to claim tax deduction for allowable sole trader related expenses - providing you don't claim the 1k trading allowance - i would have though actual expenses would be less than 1k though unless you are buying some plant or equipment though.