An article in The Economist this summer says:
The gridlock in Parliament, where mps have been caught between loyalty to their constituents, their party and the instruction of the referendum, has undermined faith in politics. The Hansard Society, a research body, finds that 37% believe the system needs a “great deal” of change—ten points more than the previous record, in 2010, when mps were mired in an expenses scandal. Willingness to contact an mp has fallen; willingness to march or join a picket has risen. More than half agree that “Britain needs a strong leader who is willing to break the rules.”
It's not clear if that last sentence points to a trend though. Are there any UK polls over multiple points time, preferably spanning the Brexit referendum vote, that shed more light on this? Basically, has the UK electorate shown an increasing preference over the last decade for some flavor of strongman rule?