I think your laughing shola i was bank approved for only €200K before any offers, a good mortgage agent should be able to push your approval out to €280k (pm me ill give you the details of mine if you want ).
but yes it happened just like that for me. arrived, shown properties, pick one, i was on my own and shown 6 different houses, a friend being offered in the same development were being shown with other couples and they picked their house a few seconds before the other couple wanted it, so id say go aerly or even have one chosen before you go.
Ps you are very likely to run in to my issues later, but thats another days work for you.