LONDON, Jan 19 (Reuters) - Rising inflation in Britain could hit demand, employment and ultimately bring down price growth, Bank of England Governor Andrew Bailey said on Wednesday. "This a hard thing to say ... but if you get pressure on cost of living, pressure on real earnings, that will tend to restrain demand in the economy... and that could lead to an output gap opening up, and it could eventually of course lead to higher unemployment and that would bring inflation down," he told parliament"s Treasury Committee. "I don"t want to suggest that ... were we to consider it necessary, we don"t have to take any action in terms of the Bank of England"s action on interest rates. We would obviously judge that ourselves. But there is another channel there which would weaken demand in the economy."