If I post a small silk scarf in an A4 letter with a first class stamp from London to Manchester. Will letter get lost in the post?

You can ask for a certificate of posting, which proves you posted it and if it got lost in the mail you can then  make a claim for lost mail along with proof and is free, or you could pay to have it registered so the PO gets proof of signature from the recipient and you can track it so you know

It may... it may not... it can... it should... it won't.

EDIT: OK 3 thumbdowners, we can not predict what the mail will do except EXACTLY as l said. 

You need to post it with a 'large' stamp which would be OK for flat A4 up to 750g. 

But it should be fine. I would probably put a bit of corrugated card to keep it flat if it does not take it over the weight.  You can send it registered or recorded delivery, 

but someone has to sign for it at the other end.

Most letters turn up, I don't  think they do tracking but you can  have it registered and signed for.

My mindreading skills are not working today.

Usually, the letter would get there.  Royal Mail processes millions of pieces of mail every day and some get lost.