The BoI, which owns Bristol & West, has taken the decision to almost double its mortgage tracker rate in a move which affects more than 13,000 customers.
The decision came despite the Bank of England Base Rate remaining at its historic low of 0.5%.
The BBC has reported that the bank will raise its tracker from the bank rate plus 1.75% to the bank rate plus 2.49%. Then in October it will raise it further to bank rate plus 3.99%.
In the letter, published by the BBC and addressed to FSA managing director Martin Wheatley, Tyrie said he was "very concerned" and asks if it was a case of product mis-selling.
In the letter Tyrie said: “It has apparently told its UK customers with tracker mortgages that in the coming months it will be substantially raising the interest rates it charges them.”
Tyrie said the BoI had increased its rates by triggering a ‘special condition’ clause in its mortgage agreements and claimed it had justified the decision by saying that banks are required to hold more capital and that the cost of funding mortgages has significantly increased.
Wheatley is due to respond to the letter today.