The figure was up on the 29,245 complaints firms received in the second half of 2010 and up from the 6,839 when the FSA started regulating mortgage firms in 2006.
The FSA data includes all the complaints firms report to it, while its firm-level data includes data from firms that report 500 or more complaints in a six-monthly reporting period.
Overall, firms reporting to the FSA received 67,309 complaints relating to home finance, compared to 64,220 in the second half of 2010.
Some 32,297 complaints were arrears related, with 2,929 relating to impaired credit mortgages, up from 2,681 in the second half of 2010.
Equity release complaints were also slightly up at 439, up from 383.
Some 45% of complaints about mortgage businesses were upheld in favour of the consumer, down from 48% in the previous period, with some £22m paid out in redress, compared to £15m in the second half of 2010.
Bank of Scotland received 12,080 complaints in the period relating to home finance with 49% upheld in favour of the consumer, while Cheltenham & Gloucester received 3,617 with 50% upheld and Royal Bank of Scotland received 2,103, with 81% upheld.
National Westminster Bank received 4,268 complaints relating to home finance, with 73% upheld, while Nationwide received 2,741 with 45% upheld and Northern Rock Asset Management received 2,616 with 44% upheld.
Santander received 8,961 home finance complaints with 42% upheld, while Barclays received 8,894 with 60% upheld.
Among the specialist lenders Southern Pacific Mortgages Limited received 858, with 35% upheld, Kensington received 813 complaints with 39% upheld and GE Money Home Lending received 730 with 28% upheld and Preferred Mortgages 682 complaints with 36% upheld
Mortgage Express also received 1,439 complaints with 39% upheld.
The overall number of complaints increased by 3% to 1,852,284 in H1 2011, with complaints about PPI up by 23% to 531,667.
The Financial Ombudsman Service also publishes data on the complaints it deals with. These are complaints referred to it by customers who are dissatisfied with how firms have handled their complaints.