Thousands of members of the RMT who work for Network Rail and 13 train companies walked out on Tuesday, Thursday and Saturday last week as part of a dispute over job cuts, pay and conditions.
The RMT and Network Rail are initially trying to reach an agreement on job security, before discussing pay and conditions."We're progressing in terms of discussions. There are some fundamental issues of difficulty between us still, and that's why we're seeking feedback, but we haven't gotten onto the question of pay yet," Mr Dempsey said.
On 20 June, the day before the first rail strike, Network Rail gave the RMT a letter inviting them to a formal consultation meeting on 1 July about introducing reforms to working practices which would involve job losses.