Rate Rise or Not?

That is a good point - It might be used by the banking sector/cartel to put pressure on the economy and rethink the Brexit strategy.

"Dovish hike" of 25bp to 50bp on the base rate. i.e they will hike but imply future rate rises will be very modest. The market has attached an 88% probability to a 25bp hike on 11-Nov which I think is too high. My confidence level is probably more like 65-70%. It's notable that by the 11-Nov-2018 MPC meeting (9 MPC meetings in total) the market attaches a 87% probability of rates being between 50-100bp so the market is only really looking for 25-75bp of hikes over the next year. 

I don't really see any domestic reason to hike. CPI is above the target but it's purely cost push rather than demand pull; there's no indication of second round effects coming into play from higher inflation expectations. Labour has no pricing power. The reason to hike is purely exogenous. Sterling has weakened easing financial conditions. Trade-weighted it's still only a 3-4% stronger than the low in late 2008. Other major central banks are tightening. The Fed is now at 1.25% and will moves rates higher slowly over 2018. ECB will start tapering QE next year. Rate differentials are going to go against sterling, which added to weaker growth than it's peers, a balance of payments problem and Brexit, all risks further weakening. As much as anything I think a rate hike is to demonstrate that they can/will hike if necessary. It's sort of cheap protection since the domestic impact of 25bp is negligible but it does impact the carry differentials which tend to drive currency bilaterals.

I don't think they should hike rates. In addition to the reasons mentioned by yangmills, there are asymmetric impacts to think about because we are at / near the lower bound. If the MPC increase too slowly then it will be relatively easy to correct by increasing rates. If they increase too quickly, then it is harder to fix as interest rates can't go any lower - they'd need to rely on QE which is more unpredictable. The fact there is so much uncertainty around Brexit makes this issue more significant.

Separately, I've never agreed with the argument about increasing rates now to give more room to cut later. If we increase too early then the equilibrium rate would be lower than it otherwise would be, meaning we would need to cut to a lower absolute level than we would otherwise to compensate. And, given we're at / near the lower bound, it may not be possible to cut rates far enough to compensate.

Rates have now risen by 0.25% back up to 0.50% (what they were last year)

I was quite obvious for a while that they will rise by the end of this year. It had to happen to catch up with inflation and recent 0.25% rise in the US, but I don't think there will be another rise for years to come.