Hi JJ,
The usual route is to get your husband referred to a consultant endocrinologist or diabetologist on a private basis. This can be pricey if you don't have private healthcare cover. The consultant will assess whether he thinks Byetta is appropriate for him, based on weight, BMI, BS levels and what other medications have been tried.
You won't be able to ask your own GP for a private prescription because there are prescribing rules governing GP prescribing. Any registered doctor can provide a private prescription, but a GP in the surgery at which you are registered can only provide a private prescription if the drug is not available on the NHS. As Byetta is available on the NHS, your GP would not be allowed to issue a private prescription for it.