You definitely should be looking at ISAs to avoid paying tax.
Coventry Building Society is offering a 60 day notice bond for the over 60s at 5.85% gross.
The same BS has a regular saver at 6% in the first year - but you can save only �2000 per month. Worth transferring from your Barclays, though!
Alliance and Leceister also do a direct saver at 5.8% gross.
So, take your time, look at ISAs and bonds as well as the savings accounts open to you. Many can be operated online, which makes things easier.