With all types of tenancy, failure to pay the rent for two months (or 8 weekly payments) can lead to a Court Order permitting eviction. A Court is more likely to grant a landlord possession for rent arrears, whatever the reasons for your difficulty in paying, than to grant a mortgage lender possession for mortgage arrears. So keep paying the rent.
Make sure you keep your landlord informed. Many of them, especially private landlords, rely on your rent for their own income, and it may affect their own finances badly if they don't receive it on time - so be courteous and let them know what is going on. In your letter, ask for a little time to sort your financial affairs out, and offer to make a reduced payment for a few months. A letter such as the example given below should suffice: