You will NOT be worse off because higher rates of tax apply only to the extent that income exceeds the relevant thresholds - typically, in your case, the £50,270 point ABOVE which Income Tax rises from 20% to 40% - but ONLY on the amount above £50,270.
To put things in perspective, someone with no other income, (or pension contributions or similar allowances)
In receipt of £45k salary + £5k "car allowance" (which is just additional salary in the vast majority of cases) will have:
Total income of £50,000 costs £7,500 Income Tax and £5,700 Employees' NICs leaving them with £36,800 after tax and NICs
Total income of £53,000 costs £8,650 Income Tax and £6,100 Employees' NICs, leaving them with £38,250 after tax and NICs
The other thing you have to be careful about, though, is if you / your partner/spouse/civil partner have children for whom either of you claims Child Benefit: it starts to be clawed back once someone's "adjusted income" exceeds £50,000 and is always assessed on the partner/spouse, etc., with the higher income (so it would not be relevant to you if you don't have children, or if your partner/spouse already earns, say, £67k - or even just £1 more than you will).
Even then, however, it is an EFFECTIVE higher rate of tax but only on the amount above £50k.
Things can become more complicated if you are offered a taxable benefit in kind as an alternative to cash, and/or if you pay into a qualifying pension scheme (pension contributions will help to save tax but it can make the calculation more complex).
I hope this is helpful.