Yes. As T acted on the consent issued by oldL (the then L), by subletting, newL is bound by that- but this applies only to that subletting and not renewals or replacement sublettings. This is so even if oldL did not tell newL about it in the sale procedure/documentation.
JEFFREY SHAW, solicitor [and Topic Expert], Nether Edge Law*
1. Public advice is believed accurate, but I accept no legal responsibility except to direct-paying private clients.
2. Telephone advice: see http://www.landlordzone.co.uk/forums/showthread.php?t=34638.
3. For paid advice about conveyancing/leaseholds/L&T, contact me* and become a private client.
4. *- Contact info: click on my name (blue-highlight link).