Adrian Flux are reputable, and well known especially for covering modified vehicles at good prices.
What is the car and how old are you? If you’re 17/ a new driver I would be considering Endsleigh, More Than smart wheels, Admiral, Aviva etc. Also try Marmalade, although I never get good quotes from them.
As someone who hasn’t got their licence yet I’ve been getting great quotes from More than.
No NCB, no named driver experience, not insured on any other car, 0 days on licence, I got £1049 on a Mini One, £1044 on a Citroen C3 and £1300 on a Vw Up GTI, yes a GTI not a normal Up!
If you’re not keen on a black box check out Go Girl (yes really)