The other day I sowed some seeds in a yoghurt pot and put them on the window sill I move them to the table at night as its warmer. Cover the seeds ligtly will compost

And don't put the plants outside until end of May.

Have a look at the Herb Expert web site :- www.herbexpert.co.uk
The main requirements are sun (haha) and warmth. As it says on the site
'If you can’t guarantee the warm, sunny conditions of the Mediterranean, it’s best to grow basil indoors'

Perhaps you could grow it in your new greenhouse, until it is warm enough outside? ......Warm outside, what a lovely thought!

yer