I'm sure The Builder willbe along to answer your question aptly... However, being as I am in the U.S. I guess I'm astounded that floor joists in the U.K. can be 2 X 4 (which is the terminology used here). The minimum floor joist here, depending on span) is 4" X 8" and more likely 4" X 10" if the apan exceeds 14 feet. Of course, most modern houses (built in the last 10 years, say) use floor trusses built from your 4" X 2", but to my knowledge, those absolutely cannot be notched or otherwise cut, since it would destroy the structural integrity.
If in fac,t your floor joists are stand alone 4" X 2", I'd find it unacceptable to cut into the joist by almost 1/4 of the width (seeing as they aren't truly 4" wide anyway). But check with your local building codes if some of the more astute (with UK laws) craftsmen don't come along...