LONDON (Reuters) - Scotland and Wales proposed changes on Wednesday to the central UK government s Brexit bill in an attempt to bed down their current powers which they fear could be weakened after Brexit. Scotland s Brexit minister Michael Russell said verbal assurances from London that Edinburgh and Cardiff would keep all their powers after Britain leaves the European Union were not sufficient due to distrust toward the central government.  There needs to be an injection of trust into the negotiating process,  Russell told Scottish lawmakers during a parliamentary committee session in Edinburgh. The EU issue has pulled the United Kingdom s four parts in different directions because England and Wales voted for Brexit while Scotland and Northern Ireland voted to remain in the bloc. The Scottish government, run by the pro-independence Scottish National Party, and its Welsh counterpart, run by Labour, have both accused the Conservative central government of failing to give them a meaningful role in the Brexit process. The EU withdrawal bill, which is currently going through the UK parliament in London, is designed to convert all existing EU laws into domestic ones. It is part of Britain s plan to provide legal clarity before it parts ways with the EU. But the bill has raised hackles in Edinburgh and Cardiff, which currently control policy areas such as health, education, transport and agriculture, because it does not make clear what the status of those devolved powers will be after Brexit. The UK government says that Scotland and Wales will be returned their devolved powers in a second phase, but that has failed to quell anxieties.  We are willing to cooperate with the UK government but this cannot mean allowing (Britain s national parliament) to drive a coach and horses through the devolution settlement,  said Russell in a separate statement.     Under Britain s constitution, the UK parliament must seek consent from the Scottish and Welsh assemblies when legislating on policy areas that overlap into their domestic powers. While they do not have veto powers over the Brexit bill, ignoring their wishes would mark a new low in already tetchy relations between London, Edinburgh and Cardiff. That could give an incentive to the UK government to incorporate at least some of the Scottish and Welsh amendments to avoid the embarrassment of a constitutional clash. Stephen Crabb, a Conservative member of parliament and former minister for Wales, told Reuters he thought there should be some room for maneuver.  UK government ministers probably have to say a bit more and to give a bit more to try to bridge the gulf at the moment,  he said in an interview. 