Time needed to change between St Pancras and Euston?

Walking takes about the same time as the tube, bus or taxi.

The most obvious route, and the one you're least likely to get lost using, is to walk along Euston Road. This is a busy main road with a narrow (but adequate) pavement (sidewalk). Depending which part of St Pancras station you want, it's usually the longer route.

A more pleasant route is to walk along Brill Place and Phoenix Road between the two stations - you will often see this offered as an alternative on mapping apps. This route involves a substantial set of steps at the entrance to Euston station, so is not an option for anyone using a wheelchair, pram, pushchair, etc. This route is about the same distance as the Euston Road route and involves much less choking on traffic fumes.

Finally, there is a true shortcut between the two stations along Dangoor Walk, but it isn't really an advertised route because it involves a number of back-alleys. This cuts about 100m off the Euston Road route between Euston and the Eurostar gates at St Pancras.

I've manipulated Google Maps into showing it here. I'd strongly suggest that anyone trying this route checks it out on Street View before walking it, because you'll be going "do you really mean to walk through this open gate into back garden of these flats?" at a couple of points (to which the answer is "yes", but you'd really want to make sure you're going through the right back garden):

Trains to Liverpool from London operate out of Euston station. For any mainline train in the UK my general rule of thumb is to be at the station no later than 15 minutes before departure for three reasons:

1. Many of the larger stations in the UK are large in size and you can find yourself on a platform a good few minutes walk from the main lobby/concourse.
2. Trains can change platforms last minute — they do not always depart from the same platform if you are a regular.
3. Trains doors can close up to 5 minutes before departure.

With a connection I would leave at least 30 minutes leeway for any potential delays on the Eurostar.

Regarding your situation. You won't make this connection. I would get an earlier tube to Euston station to make this connection or get a later train to Liverpool. The advertised tube times are the times they will stop at the platform. The tube network is vast and from Euston will take you several minutes to get to street level. St Pancras - Euston is however very walkable (about 10 minutes down a straight road) Turn right out of St Pancras main entrance and head down Euston Road past the Unison HQ. Euston station will be on the right hand side behind Euston Square Gardens. You can't miss it.

If you follow the research the above users provided then you should be fine. However, if you know you get turned around easily or are a stressful traveler, it's best to allow for more time. Assume that any time you're going somewhere new as a tourist that it will take twice the time. This will allow for time to ask for directions or clarifications if you're nervous.

I traveled alone in the UK last February and I should have left a bigger time buffer. Plus, you'll be at King's Cross. If you like Harry Potter, they have a shop and photo station. The line up can be massive though.

The walking route between these two stations has now been designated the "Wellbeing Walk" and has signage so it is probably not necessary to even have a map with you. Nonetheless the web site for Urban Partners about the walk does have a map.

Many of the other answers are assuming you arrive at St Pancras International by Eurostar, and advise you to allow more time. If that is not the case (e.g.: because you are arriving on a Southeastern High Speed service or an East Midlands Trains service), I would say even 20 minutes should be more than enough to walk, with luggage, (I would not advise getting the Underground for that journey, because getting to the Underground platforms entails a long walk and escalators) from St Pancras International to Euston and find the correct platform at Euston (NB: for Virgin Trains services, the platform gates close two minutes before departure). Of course, if your previous train is delayed, that might become a problem (check https://www.recenttraintimes.co.uk/ to see historical performance)...

Any of the walking routes mentioned in other answers will be slower if you are dragging a bag behind you. However, the same is true of using the tube. Many train tickets when booked in advance are for a specific train at leaving a specific time, and if you miss it your ticket might not be valid on the next train.

Best advice: leave yourself longer than a very tight 25 mins. You can always dawdle a bit to get your bearings, visit a nearby attraction, or get something to eat or drink.