Fed, ECB and BoE don't need to hike rates again, the money market has already done it for them a few times over.
big issue with the disparity between cash market and derivatives is that big banks hedge their cash exposures in the derivatives (swaps are following the FFs)- hence if the two are moving in different directions hedging is not possible, exacerbating the problem.
Libor normally trades at 3-10 bps above base rate for overnight. maybe 15-20bps over base rate for 3 month. Last Friday GBP was at +100bps for 3 month.
That's the quivalent of 4 BoI rate hikes in August alone.
Given that most corporates borrow in 3 month paper, and most variable mortgages are based on 3 mth Libor, the 3 month Libor rate is the ACTUAL cost of borrowing, the base rate is just a benchmark.