TL;DR: doing this is highly likely to lead to your eviction. Don't do it.
We have a large living room in the flat which we are considering renting out on AirBnb (this could save us as much as £400 each a month on our rent). But does this count as subletting?
Yes. As this comprehensive article explains, it likely places you in breach of your tenancy agreement (which is almost certain to prohibit subletting and the like), as well as breaching your landlord's insurance policy, and possibly placing them in breach of licensing regulations.
We would not be entering into a tenancy contract or agreement with any potential guests.
If money is being exchanged for a service, then a contract exists, whether or not it is written down. Also, as user6726 mentions in their answer, AirBnb are explicit that a legal agreement exists if you act as an AirBnb host.
What repercussions could we face?
The landlord could take eviction proceedings against you for breaching the tenancy agreement. Or, if this is discovered once any fixed term has ended, they could issue a section 21 ("no fault") notice to request that you leave, without having to state any reason.
Could the landlord demand we pay all profits made from this 'venture'?
No. The only money that a landlord can demand from a tenant is to cover (a) unpaid rent, and (b) at the end of a tenancy, restoring the property to its condition at the start, which could include repairs (for damage caused by the tenants or their guests) and cleaning - but excludes wear & tear.