The intensive recovery programme, involving 8,000 engineers at 60 sites, was aimed at repairing 25 miles of track.
But Mr Prescott told the BBC that about 40 miles had been replaced during the holiday period.
However, commuters returning to work after the seasonal break had to cope with delays and cancellations after Railtrack failed to complete two major re-signalling projects in time.
The firm said engineering work over the holiday period meant 80 speed restrictions imposed on the network since the Hatfield crash had been removed or eased.
Mr Prescott said Railtrack is now on target to return 85% of services to normal by the end of January and 100% by Easter.
"I think passengers will be glad to hear that the recovery programme we set out a month ago is now being delivered," he said.
Mr Prescott went on to thank, on behalf of passengers, "all those people who have worked extremely hard in the most difficult of circumstances to make the improvements".
But people returning to work on Tuesday faced widespread problems after engineering work planned more than a year ago lasted longer than scheduled.
Work still being carried out in Willesden, north west London, forced Virgin to cancel trains on its West Coast route while local services were delayed more than 15 minutes.
East Coast main line operator GNER is using buses to take passengers to Wakefield because of re-signalling work at Leeds.
Bad weather and "technical issues" had hampered their operations, he added.
The firm's chief executive Steve Marshall said: "We recognise there have been some problems and that Leeds and Willesden are not completely finished.
"But the Christmas and New Year engineering work generally has gone extremely well.
"Many people have been working around the clock over Christmas and the New Year to make sure that rail services improve.
"Everyone at Railtrack knows no effort can be spared until the network is fully restored."
New timetable
Many train operators are still running a restricted timetable until the end of the week.
But Railtrack said travellers could rely on faster and more reliable journeys when new timetables on affected lines come in on 8 January.
The previous day some train operators are due to increase ticket prices above the rate of inflation.
Passenger groups have condemned the move as "insensitive" to travellers who have had to endure endless disruption since the Hatfield tragedy, in which four people died.
Mr Prescott accused train companies of showing indifference to their passengers and asked the Rail Authority to look into the fare increases.
Low confidence
But he stressed that regulated fares had seen a reduction in prices.
Lack of public confidence in the railways forced many travellers to turn to coach and air travel for their Christmas journeys.
National Express reported an increase of between 15% and 20% in passenger numbers compared with this time last year.
Railtrack has cut its figure for predicted passenger growth on the railways from 47% in 10 years, to 37%.