* Graphic: sterling and gilt yields http://bit.ly/2dgAXn1
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv
* BoE says UK banks can handle bad Brexit
* Teetering Irish govt latest headache in Brexit talks
LONDON, Nov 28 (Reuters) - The pound slipped from a two-month high on Tuesday, having failed to push above $1.34 against the dollar as Brexit-related doubts began to re-exert their grip on the UK currency.
Sterling was back below $1.33 and flat against the euro and the yen at 0.8989 pence per euro and 148 yen respectively, as markets headed towards mid-morning.
There had been a brief flurry of interest as the Bank of England said UK banks could handle a bad Brexit in its annual health check on lenders, though there were more than enough difficult questions to offset any enthusiasm.
A deal on the Northern Ireland-Irish border - a key part of Brexit talks which were hoping to see a breakthrough next month - has become trickier as the Irish government has been pushed to the brink of collapse.
The country's opposition party propping up the minority government has said the deputy prime minister's refusal to quit over handling of problems in the police force would force the country to the polls next month.
A motion of no confidence in the minister in question, Frances Fitzgerald, is due at 2000 GMT on Tuesday unless she quits. But Irish national broadcaster RTE cited a minister as saying Fitzgerald had decided to step down.
"The EU has given the UK government a deadline of next Monday to come up with a plan on the Irish border, so that seems to be the main sticking point now," said Societe Generale FX strategist Alvin Tan.
Whatever happens with Fitzgerald, if the deadlock between London, Dublin and Brussels over the already complex and politically sensitive border issue does keep Brexit negotiations stalled, that could spell trouble for the pound.
"In that situation, I wouldn't be surprised if we see cable (sterling vs dollar testing the August low of $1.30 again and euro/sterling re-testing of the 93 level again," Tan added, although he also said it could be a buying opportunity.
Sterling was buying $1.3295 as midday approached, down 0.2 percent on day. It is just about clinging on to a monthly rise against the greenback though it has seen is nearly 2 percent drop against the euro in November.
As well the Bank of England saying that UK banks could handle a "disorderly" Brexit on Tuesday, for the first time since it started its stress test exercises in 2014, all avoided bills for more capital.
Responding to a question about whether there were signs that Britain's large current account deficit was unsettling investors, BoE Governor Mark Carney said foreign capital flows were continuing to come to Britain though a disorderly Brexit would most likely hit the economy and sterling.
"Our job is to maintain monetary and financial stability in whatever scenario, and with that bedrock one can expect that you build off that bedrock to continue to see foreign inflows as we should," Carney said. (Reporting by Marc Jones; Editing by Hugh Lawson)