On a tax return, do the Inland revenue accept bank statements as proof of business expenses? Or only receipts?

In the UK.

Band statements do not give detail of the purchase so would not be of much use in proving chargeable expenditure. Invoices are your best shot.
Anyway, the Revenue normally only check such detail if they suspect all is not as should be. Honesty is the best policy to build trust.

In the US, they would want receipts.

Your Tax return only asks for totals not individual expences, unless you are being checked out ty wont want to see the individua transactions, IF you are then its best to come clean and provide absolutely everything. You dont want to end up with full investigation.

Remember the Inland Revenue's motto
"You are guilt until you can prove otherwise"

You will need receipts for everything or there is no way to tell wht it was that the money was spent on.
This should apply even to items such as Direct Debits arrangements for say a mobile phone contract where you will need a copy of the agreement and other proof of the payments.
I have been self employed for 10 years and I have a receipt for everything that I need to claim against tax the Tax man gets enough as it is why give him the oipportunity to get more than he deserves.

If they require evidence of expenditure(very rare unless you are under investigation) they will require receipts. But they will accept credit card statements if expenses are paid that way, and it is clear what the expense is. eg petrol.