What £370,000 means for your stamp duty bill
£370,000 puts you into the 5% band, which applies to the slice above £250,000. Your total of £8,500 works out at an effective rate of 2.3% — well below 5%, because the first £250,000 is taxed at 0% and 2% respectively.
First-time buyer relief is worth the most in this bracket. If you qualify, you would pay £3,500 instead of £8,500, a saving of £5,000. That relief vanishes completely above £500,000, so it is worth checking your eligibility carefully before you agree a price near that ceiling.
For context, £370,000 is about 28% above the UK average house price of roughly £290,000. Your marginal rate at this price is 5%, meaning that is the rate charged on the next pound you add to the purchase price.