I don't think there's any CGT because the value of the house has fallen since the parents inherited it themselves
If it has fallen below the indexed value (inflation adjusted) when the parents adjusted it then you may be right, if the value has simply fallen by a cetain amount that doesn't matter. If the house isn't your boyfriends parents principal private residence (more or less the house they live in all the time) they will pay Capital Gains Tax on the deemed market value (they can sell it to your boyfriend for any amount but for revenue purposes the market value will be used) less the original value indexed.
I'll use these numbers as an example.
House inherited in 1986 at 200,000
Market value now 460,000. Parents gift the house at 360,000.
The 200,000 is multiplied by an index factor to take into account inflation, I'll use 1.5, so we get 300,000. Take this from the market value and you get 160,000 at whatever the tax rate is. If it's the house his parents live in then they pay no capital gains tax if it's a second home they will.
For gift tax there are certain amounts that can be transferred tax free to a child with no tax implications, any portion of the house gifted to you will be taxed.
This is what i remember from doing tax ages ago so it's worth getting as much info (especially about the house in question) as possible and thinking of a couple different scenarios and go to an accountant.