As suggested I am not convinced that my partner having a DNA test would have the answer. Any suggestions please.
You would be surprised at the results a DNA test can give. Whilst it may take a little time for it to propagate a result that is worth looking into, it is your best bet especially when looking for a biological parent that you are unsure if it is correct or not. Many people have had success if finding biological parents of ancestors using DNA even to find out who they thought were biological weren't.
Additionally, there are few records available for 1954 that would show you whether the said person was living where you think as they are not released yet, and even if there were, wouldn't necessarily show if your partner is related to him or not, hence why a DNA test is the best route to take.
That said, where did you get the information regarding him living in Coventry Road, Birmingham? I ask, as looking at the 1939 census (the closest released record bar directories to the date you provide and available on Ancestry), it shows a William Wright living in Coventry, Warwickshire, England (not Coventry Road), born 1916 and had an occupation of Aero-Carburettor Fitter. This is another candidate further to the one Antony mentioned earlier.
Now, I am in no way suggesting that this is the person you are looking for as there are inconstancies to the record and your details i.e. born 4 years later, not living in Coventry Road but Coventry and also there are many types of 'fitters', but perhaps may be someone to look into and perhaps if you do get a DNA test, someone to keep a look at for in the results.
Just keep in mind however, that even if you do look into the above mentioned person or any other possibility, there is no guarantee it is the biological father unless you can find an actual record stating your partner is related or a DNA test can prove it.
