Work on four routes serving Bristol, Oxford and Berkshire is now on hold.
Rail minister Paul Maynard said it would free up money to "deliver additional benefits to passengers" and added Wales would not suffer delays.
"My focus is to ensure that we deliver electrification to Cardiff on time," he said of the £2.8bn modernisation plan.
Responding to a question from Cardiff West MP Kevin Brennan during a Commons rail debate, Mr Maynard said he wanted to make sure "that passengers in south Wales benefit from that electrification to the fullest degree possible".
Network Rail also gave assurances on completion of electrification between London and south Wales.
Wales route managing director Andy Thomas said: "We are working to build a bigger, better railway for Wales, with electrification of the mainline to Cardiff expected by 2019 as part of our Railway Upgrade Plan.
"Electrification between Cardiff and Swansea is planned to be completed by 2024, with dates and costs to be confirmed.
"However, passengers in Wales and across the borders will see the benefits far sooner with the introduction of new Intercity Express Trains between London and Swansea from summer 2017."
Meanwhile Cardiff North Conservative MP Craig Williams has welcomed additional assurances from Mr Maynard about improvements to Cardiff Central station.
The ability of the Welsh capital's main transport hub to handle big events has been questioned following long queues and delays during the 2015 Rugby World Cup.
"In addition to improving the rail network it will complete Cardiff's Central Square and strengthen the transport interchange for our city," Mr Williams said, leading the debate on Tuesday.
"The huge projected increase in passengers is good news but Cardiff needs a redeveloped station to cater for them".
Electric trains are still due to start running between Cardiff and London in 2019, a minister has said, despite the deferring of work on other lines.