You can put just ‘HMRC’ (UK tax department) on a letter (with paid postage) and it will get to them.
So presumably...
<MP name>
HP
...with no stamp on the envelope could theoretically work.
Now, which MP has the shortest name?
I daresay "A Mak" or "R Huq" would work too.
PM
HP
Might work. Maybe I should go and parcel up some dogshit and try it.