I am travelling to Canada with layovers at London and Dublin ( Mumbai - London - Dublin - Canada) with British Airways. I have an Indian passport and Canadian Student Visa. Both the layovers are below 3 hours. Will I be requiring a transit visa to catch the connecting flights from these airports? Ticket is on same booking id with same airlines.
This poster from the Home Office says that you can transit the UK landside (and that transit to Ireland is always landside) without a visa if you hold a valid Canadian visa and "a valid airline ticket via the UK as part of a reasonable journey TO" Canada.
According to http://www.inis.gov.ie/en/INIS/Pages/visa-required-transit you will not need an Irish visa if your connection is airside (does not involve passing through Irish border controls). BA can tell you whether this is the case.
If this does not apply to you (i.e. if you have to pass through the border controls to catch your next flight) then you will need a short stay visa.