As a grad, the only think different for me was better performance on entrance tests... From 0 interviews one year to 4 the next just because of the UKCAT.
Were you rejected before or after interview? Also, were your choices suited to your strengths? e.g. lots of A*s at GCSE, Birmingham, good UKCAT King's etc.?
If you were rejected after interview, it could have been interview performance, some places give feedback on this, or it could have been lack of insight, say, for which more experience would be great.
Either way, I don't think extra experience would be anything other than beneficial, but there may be other areas your application could be improved in.