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If it is one ticket then BA will rebook if despite best endeavours you miss the check-in deadline in T5.
Three hours is reasonable for the connection, assuming all is well. Depending on time of day / roadworks and your baggage situation you may prefer to take the train, but if the coach service is working and traffic is flowing then you should have a reasonable connection in my experience. See also the main LHR-LGW thread in the BA Forum Dashboard for timings and the various options open to you.
I would query if you can find a similar fare via LHR or from say NCL. It's unusual if this is cheaper than starting in LHR.