He should be able to get his adoption file - follow the instruction here
https://www.gov.uk/adoption-records.
That should give his birth mother's name, if it isn't on the original birth certificate.
Also, I would suggest Autosomal DNA testing, firstly at Ancestry as it has the biggest database. This is because I have worked with adoptees whose birth mother gave a false surname on the adoption records.
After doing DNA at Ancestry, upload the raw data to as many places as possible (My Heritage, FtDNA, Living DNA etc) and also test at 23&Me as they don't allow uploads from other sites.