Scarifying is fine, and combined with re-sowing and feeding, will improve the lawn, but you may find that controlling moss with sulphate of iron and then feeding will produce better results.
My garden is very mossy. High trees used to surrounded it, but last Summer I removed them – it now gets more light and sun. I applied 7:6:17 two weeks ago and today used a scarifier and spread lawn seed afterwards on top of the freshly scarified lawn. Was this the right thing to do and is there anything else i need to do now, or just wait? What other feritlisers should I use into the summer?
Reducing shade will certainly reduce moss growth and feeding is essential to encourage grass growth to compete with moss. 7-6-17 is a general fertilizer which is fine for a once-off treatment but is too low in nitrogen. Use a lawn fertilizer or a high-nitrogen fertilizer in spring and summer.