The answer depends upon when the lease was granted. For leases granted before 1996, the original tenant remains legally responsible for the rent and the other lease commitments for the duration of the term (even after it has sold its interest).
For leases granted after 1996, the position is different. The tenant ceases to be liable to the landlord for future breaches once it has sold (assigned) the lease. However, landlords can legally require the selling tenant to guarantee the new tenant’s lease obligations using a guarantee document known as an Authorised Guarantee Agreement or AGA. It is important, therefore, when selling leasehold property, that you are happy with ‘covenant’ strength of your buyer.
The law in this area is complex and still developing and it is important that you get legal advice regarding your on-going liabilities when selling (assigning) a lease.