Did you renew your travelcard this week, as you prepared for a new work year? Did the cost make you want to cry? You're not alone.

#RailFail trended on Twitter on Tuesday (2 January) as many people returned to work after the Christmas holidays, only to discover average rail fares across the UK had gone up by 3.4% – the biggest increase since 2013.

Commuters protested at 40 stations across the UK as Bruce Williamson, from campaign group Railfuture, said people were getting priced out of going to work. He said British rail fares were some of "the most expensive in Europe".

The Department for Transport said it is investing in the "biggest modernisation of our railways since the Victorian times" and that fare rises were capped in line with inflation. Yet it might be cheaper to go on a European vacation than to just travel to work every day.

How much do UK travelcards cost?

As eight out of the 10 most packed services in the UK were London commuter trains in 2017, we have looked at some common London commutes for this exercise, working upwards in price. These prices do not include travel within London once you reach the city – travelcards in the capital have also gone up.

Southampton Central to London Waterloo costs £451.20 for a monthly travelcard – £22.56 per daily return if you travel on 20 working days. That journey is around 81 miles.

A Peterborough to London King's Cross monthly travelcard costs £627.90, or about £31.40 per daily return, for around 84 miles.

Bristol Parkway to London Paddington costs £1,126.70 per month – around £56 per day for 115 miles.

A Leeds to London monthly travelcard is £1,385.10, which works out as £69 per day. That journey is about 195 miles each way.

And a Newcastle to London monthly travelcard would cost 1,889.30 – about £94.47 return each day for 280 miles.

Is return trip to Europe really cheaper?

For most of the train journeys mentioned, a quick trip over to many European cities is indeed likely to be cheaper in comparison. This month, for example, you could go for a short break with return to Milan from London Stansted for £29 with Ryanair, or Prague for £34 return, both around 800 miles away.

You could also travel more than 1,300 miles to Lisbon with Ryanair for £49 return, and Easyjet could take you to Munich from London, 710 miles, for about £66 return.

People are beginning to realise how much cheaper air travel can be.

George Aylett, chair of University of Hull's Labour Club, claimed it is now cheaper to fly from Newcastle to London via Spain than it is just to get the train. A quick check on Skyscanner shows that you can travel from Newcastle to London via Dublin for £50 on Monday 8 November, or £25 if you book three weeks further in advance. A direct train journey would cost at least £117.50 if you wanted to leave before 8am, or £46 to £54 off-peak.

Another Twitter user noted that it would be cheaper for him to fly to Munich and back than to travel from Nottingham to Edinburgh on the train for £133. That claim seems fair, as Skyscanner shows return flights this month from Edinburgh to Munich from £91 (Nottingham's nearest airport, East Midlands, does not fly to Munich).