A Bristol & West spokeswoman said interest would be credited from the day after the investor's cheque was received.
One Independent reader complained that her deposit in the Fixed Rate Bond account was acknowledged on 28 July and she was still waiting for her passbook three weeks later.
The spokeswoman said applicants should now be receiving passbooks within a week of receiving acknowledgements for their deposits, which in turn are going out within three days of receipt.
Scarborough Building Society's First Post account can now be opened with a minimum of pounds 250, reduced from pounds 1,000.
Norwich & Peterborough Building Society is raising rates on its Postmaster account by 0.2 percentage points.
The account now pays from 10.25 per cent gross (7.68 per cent net) to 10.8 per cent gross (8.1 per cent net).Reuse content