[Avulon]

Are you sure that the 3 pipes on the tank aren't in, out and vent? And that it's actually an expansion tank for the closed circuit heating system to heat the hot water in the 'normal' hot water tank? Not sure how that would be cross connected with the gas ch closed circuit but I guess it's possible with temp sensors and servo operated valves. But importantly, if I'm right, it's there for a very good reason. That reason could be to prevent terminal pressure build up (prevent a steam explosion). The log burner cannot be simply turned off when the hot water system is at max temp like the gas boiler can. In the old days of back boilers with open fires the heat from the fire could be directed to effectively control how much heating went into the system. This isn't going to be likely with a coil from a log burner.
I'd definately suggest consulting an expert on log burner integrations with c.h systems before even thinking of removing the large tank. You need to be absolutely clear of it's purpose before you can judge if it's necessary or not.