Second British visa application - proof of previous visits

We reside in Ireland and, as non-EU citizens, require a visa to travel to UK. Which we successfully applied for and are now traveling, naturally, as tourists. But there is one potential issue with that.

Not sure about other countries, but if you travel to UK from Ireland by practically any means, no one ever checks your passport. And of course never stamps your passport. We confirmed that while driving (Northern Ireland) and flying (London area airports). Yet to be confirmed with ferry (Wales), but everyone says it will be the same. According to Internet passport checks do happen, but on a rare occasion. Did not happen to us yet.

Having dealt with visa applications in the past, I know that many countries pay very close attention to your previous use of their visas. That is, if you want to receive a second visa, you need to prove that you have used a first one properly. This can be easily proven with stamps in passport signifying entry and exit, and I did have experience with other embassies when these stamps were indeed used for that purpose.

Now because of the situation with crossing British border I described above, we may end up not having a single British stamp in our passports, despite multiple travels. So my question is - should we be worried? May this become an issue for us if we want to apply for a subsequent British visa (or even perhaps visas of other countries)? Should we be starting collecting some other proofs (shop/hotel receipts, used tickets)?