The simple answer is, yes. It is unlikely that the landlord would choose to have an empty building rather than receive some rent – even if the rent is less than the landlord would like.
If the landlord accepts a lower rent, they might like to look at it again after a period of time to make sure it is still fair to both parties. Almost all leases will provide for periodic rent increases, but the way in which the rent is reviewed will vary. It may be suggested that the rent will be increased to 'market rent', or by any increase in the Retail Price Index. An increase to 'market rent', which may be suggested in a case where a lower rent is accepted at the outset, will often be agreed by the parties as being the rent that is appropriate for those premises after taking into account recent lettings or rent reviews for similar properties in the same area.
Market rent reviews, with cost and time implications, are not always popular for short leases or where the rent is not particularly high. For that reason the parties often agree to increase the rent by RPI each year.
Lower rent is not the only option though. If the rent is to remain the same then you may suggest a rent-free period at the commencement of lease, say three months rent free on a shorter lease. A rent free period effectively reduces the rent – and it also helps a tenant during the early stages of setting up a business or moving premises.
Sometimes the landlord may be willing to make a contribution towards the cost of the tenant fitting-out the premises. As with the rent free period, this is a cost the tenant will not have to pay, which is a saving that can be offset against the rent.