Some explanation is needed here.
Do the cheques bear your signature or have they, for example, been given to you by someone else? If they carry your signature then I can see no reason why you can't countersign them and get the cash (although, if they're not sterling cheques, you might possibly need to go to an independent bureaux de change, rather than to a bank).
If the cheques carry the signature of someone else, irrespective of whether they've then been countersigned by that person, you can't cash them. In the USA (and in some other countries) many traders are happy to accept traveller's cheques in payment for goods or services because, once they've been countersigned, they effectively become banknotes which can be paid into a bank. In the UK traveller's cheques can't be used to pay for goods or services (because banks won't accept cheques which have already been countersigned); they can only be cashed at banks or bureaux de change. If you've got cheques which haver already been countersigned, they have no value in the UK.
So what reason has the bank given you for refusing to cash the cheques?