Scarifying Mid November

I contacted a local lawn care company in September when I moved in my new house with regards to scarifying, aerating and seeding my lawn and booked them in to carry this out.
Anyway I never heard anything back up until yesterday when I received a text saying they will come tomorrow and carry out the work.
Now I'm no expert with lawns, in fact I'm a complete newbie to gardening, but all I have read is that scarifying should take place in September/October so it gives the lawn chance to recover before winter. So with my limited knowledge I told them I didn't want it doing now as it is too late and I will wait until Spring. They did say it is absolutely fine to do now and they maybe correct, but it concerns me a little that it may not have chance to recover.
They are the experts so what they say should be correct, but I have still refused as there is a part of me that thinks they may just go ahead to take my money wether its a suitable time or not.
I have probably done the wrong thing but I followed my gut instinct. What do people think with regards to scarifying now? I do live near Cambridge and the weather is fairly mild.
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I was thinking of scarifying my lawns in the next few days. Unless someone tells me I shouldn't?
It depends on your local weather conditions. Normally by now we've been frozen and can be experiencing heavy gales and storms so no, I wouldn't scarify this late.
However it's been so mild here with little wind and rain and very warm days that I would scarify if it hadn't already been done earlier.
If it's warm enough for the grass to grow and still need cutting, it's OK to scarify but make sure you have a few mild days forecast for it to recover a bit and get in at least one more cut before the weather closes in..