You can scarify earlier than April you live in London its much warm down there you could possibly weather permitting do it early march ( I do mine normally mid March NW ) you'll know when to scarify when the grass is starting to growing.
Your lawn looks good to me from that picture for the time of year.
After killing the moss and scarifying I would then sow your grass seed - top dress ( I assume that what the sand/soil mix is for , no mention of aerating the lawn ) and final add the fertiliser , you fertiliser most not have anything for kill weeds it not advised for new grass , look into lawn weed killers late April /May unless you do it by hand.
Whats in the grass seed you've bought ? probably high dwarf perennial ( lolium perenne ) and what else ? I see a lot with strong creeping red fescue which it a cheap filler and not ideal for a ornamental lawn .
It's hard to get good grass seed from retailers... I know the OP has already bought theirs, and it sounds fine for the job. I always refer people to suppliers that sell to trade and the public.
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Your lawn looks good to me from that picture for the time of year.
After killing the moss and scarifying I would then sow your grass seed - top dress ( I assume that what the sand/soil mix is for , no mention of aerating the lawn ) and final add the fertiliser , you fertiliser most not have anything for kill weeds it not advised for new grass , look into lawn weed killers late April /May unless you do it by hand.
Whats in the grass seed you've bought ? probably high dwarf perennial ( lolium perenne ) and what else ? I see a lot with strong creeping red fescue which it a cheap filler and not ideal for a ornamental lawn .