Lily-mae, It all depends on weather conditions in Late May/early June. There are two aspects to consider.
Firstly you always want to avoid moving tender plants outside from their lovely warm growing conditions to cold outdoor conditions that could cause a shock. Of course we always need to harden things off, gradually acclimatising plants to cooler outdoor temperatures, but cold conditions can really stop growth in its tracks. There's nothing to gain putting plants out a week or two early, but lots to lose!
Secondly, growing conditions in a greenhouse will be so much better, that an extra fortnight under cover helps plants put on so much more growth than they would achieve outside (both above and below compost). I'm a great advocate of keeping plants under cover a little longer to help them grow to a bigger size before going outside. At this time of year you can almost watch the plants grow each day.
I hope this helps.
