@FizzyPink
Tube will be easiest. Kings cross to Green Park on the Victoria line, then change to the Jubilee from Green Park to Wembley Park.
It will be much quicker than a bus or taxi
If there is a rail replacement bus for the Met line closure, there will be signs in and outside the station and staff to help. It will be simple and just a few stops to Baker Street, where the line is working. It will probably take about 20 mins, not much faster than walking!
If there isn't a replacement bus. You can get the 205 or 30 bus to Baker St from outside Kings Cross. The numbers are displayed at the bus stops. All the bus shelters will have a poster with a map of the area showing the bus stops, a list of all destinations from the area that gives the bus number you need and the location of the bus stop. Again, it will take about 20 mins.
Alternatively, you could get an Uber to Baker Street for about £6ish or Wembley. You can see the price on the app now without booking but it does vary day to day with surge pricing. Or you could get a black cab (very expensive). There is a rank at Kings Cross, it's signposted.
FizzyPink's route would be the easiest and cheapest route, despite the slight detour because of tube closures. It's hard to get lost on the tube.
If your mainline rail ticket doesn't have a travelcard included, the cheapest way to pay is using a contactless bankcard. Just tap the Oyster reader once when you get on a bus, not when you get off. You need to tap the reader twice, in and out at the barriers, on the tube.