Hi,
I definitely agree with Bookbox that knowing where to look would be much easier if you knew where he offended/which court heard the case because “Surrey/London” is, indeed, an extensive area. However, I’m not so sure there are no viable search strategies – that really depends on how much effort you’re prepared to make. You do, at least, know the year and that narrows the field.
So, bearing in mind that not all newspapers are online (yet), perhaps you could try Surrey History Centre – which holds back issues of newspapers – or the British Library's newspapers collection? I've found several things in newspapers that aren't online by visiting the BL. It would mean spending possibly a considerable amount of time carefully trawling through papers without any guarantee of success but, hey, nothing ventured nothing gained!
As a starting point, if you google "surrey newspapers backissues", you'll find a Surrey County Council page which lists past and current local papers. You could then use the information gleaned from that to search the catalogues of Surrey History Centre and/or the British Library, to see if they hold the papers you want to look at.
I don't know where you're located but if visiting either of these two isn't possible due to distance, you could try posting a lookup request on Rootschat - some kind soul might take a peep at the papers for you. (Provided you've done the groundwork by searching the catalogue(s) and say exactly where to look.)
One last thing: If I were you, I’d search from, maybe, 1907 onwards because it’s unclear how much time elapsed between committing the theft and being convicted by a court – then being discharged by the RAMC.
Good luck,
theirchild.