I have two washbasins upstairs, one in bathroom and one in bedroom. They are about 2feet apart. On the outside wall I have a 32mm waste from the bedroom which picks up the bathroom 32mm waste using a 32mm push fit 'T'. From there, I have about 6feet of 32mm pipe to the drain.
When I fill the bahroom basin and empty it, I get gurgling noises in the bedroom which is the furthest washbasin from the drain. I understand that I am getting an air suction/ venting problem when the bathroom sink empties. Is the easy cure to replace the last 6feet of pipe with 40mm pipe and a 32/40mm connector from the existing 'T' or will I have to get a 40mm 'T' and reducers to both wastes?

fit the basins with anti vac traps.

Thank you hi-spec plumbing and heating for your promp reply. As a complete novice, I replaced all my old leaking cast iron pipes and ended up with the gurgling problem when i went over to a much thinner 32mm piping. I never realised there was such a thing as a basin anti vac trap. Many thanks for your help here, will buy you a beer next time you are in Harrogate!