Can anybody help me. My passport expired on the 13th of this month and I'm planning on going to France via channel on the 27th. Will they allow me across with an expired passport or will I have to get a temporary passport? If so, how do I purchase one? Any comments are really appreciated.

Contact your passport office for an appointment. You can get a renewal quite quickly, but it will also be quite dear.

Everything you need to know is here: https://www.gov.uk/government/organisations/hm-passport-office
You CANNOT travel on an expired passport, there are NO temporary ones any more.
You CAN pay for an express ONE day service in person at one of the passport offices.

Agreed, you renew your passport, and as noted can not travel without it being current.

... planning on going to France via channel ...

Assuming OP is in the UK, how else would one go to France, other than by crossing the English Channel?

A Tardis?

One could also fly across the Atlantic, America, the Pacific, Asia, and Eastern Europe, and arrive in France from the East, but why?

@AK. That is a given. OP is in UK, obviously. I wonder why he didn't say he was going via the 'Chunnel'? Unless he doesn't care for being under the British channel.