UK bank account number and sortcode checking algorithm needed

one might write an app that submits a number to the  online tool

If you intend to do this as a business concern, then I would STRONGLY recommend buying the list. You'll get regular updates to it and you will have legitimate access to it. I suspect that if you do write an app to validate via an online tool and you use it a lot, you'll be blocked. Especially if there is a paid for service!

I'm pretty sure that account numbers/sort codes can be checked for validity with an algorithm (obviously this doesn't check if they are live accounts or not).  Try going here: http://www.iban-bic.com/iban_und_bic.0.html?&L=2 and putting valid/invalid account details in.  I put my own account details in and was told it was valid.  I then changed the last digit and was told that the checksum failed.  The word 'checksum' says pretty strongly to me that one of the digits in the account number is a check digit....  

Thanks for your help but I've found the answer here:  http://www.ecbs.org/Download/tr201/UnitedKingdom.PDF

Nice file. Just remember that because it is passes a checksum doesn't mean it is valid. That is why there are lists you get from the bank.

I just need it to check for typos at this stage rather than live accounts so should do the trick. Cheers for your help anyway.

NP.

I'm assuming from your solution that you are trying to validate these cards and then processing payment offline, maybe putting them manually through a PDQ machine.

If the volume of orders is low enough for you to cope with that then that solution will work.

My attitude is always to think bigger.  Your website could increase your reach and so you WANT it to be able to handle as many orders as possible as quickly and securely as possible. For you and the customer.

If you're that small you don't HAVE to be PCI compliant but it looks good if you are.  If you're not storing the customer card details properly you're leaving yourself open to a whole can of worms in the future. Not necessarily from hackers but dishonest employees too.

I would always go with a payment gateway solution.  If I was a customer and I realised that my card details were just going to sit in an unprotected database or in someones outlook folder I would be horrified and never do business with them.

Think carefully whether this is even the correct solution to the problem.

these things are verified online. Try signing up to a merchant that does online verification like www.itransact.com . Their advisors would contact you and you could liaise your requirements and other details.

Why dont' you just authorize the details with your acquiring bank and get them to check it all for you in real time?  Or perhaps if you use a service provider than an API is provided that checks this all for you anyway.  
As crmapley suggests, it is likely you will fall under PCI DSS if you are processing credit/debit card numbers.  You'll save a headache by outsourcing and paying the 3-4% commission?