Welcome to the Wefugees Community and thank you for your question.
In general, it's possible for couples to marry no matter what their legal status is. Of course there might be complications e.g. if they are afraid of getting in touch with authorities because they fear deportation etc. In this specific case, however, they are still awaiting their cases to be decided and therefore can't be deported in the meantime. So if they can provide the required documents, they should be able to marry. Please check out the following website provided by the British government for extensive information:
Apart from that, have you gotten in contact with the register office to ask them about the exact requirements and procedure? If there are certain details to be kept in mind that I couldn't find information about, they are the ones that can give valid advice about it.