Hi there Jack,
Sorry if I'm a bit late coming to this but you use the card itself for the ES (coupons not valid), last time I checked it was about GBP29 STD and around GBP50 in Standard Premier to either Calais, Paris or Brussel. Current fares should be on the ATOC/RSTL website as Jonathan says.
There is one direct TGV duplex (TGV 9577) each day from Paris Est (a ten minute walk from the Eurostar Terminal at Paris Nord) at 15h55, arriving into München Hbf at 21h26.
It runs non-stop across the Champaign region to Strasbourg at 300KM/H before crossing the Rhein and the views from the bar on the upper deck are great (particularly when you have a class of rosé in your hand!)
Going the other way TGV 9576 leaves the Hauptbahnhof at 06h46 and arrives at 12h33 in Paris.
There is limited availability for FIP places on these SNCF/DB TGV/ICE France-Germany trains where again like Eurostar coupons are not valid as they are classed as "globally priced" trains.
Last time I used that train was in Mary of last year and it was EUR15 in Second class and EUR30 in First (which I believe includes a light meal and drinks as on Eurostar), but this is only available if you have a First class FIP card. You can book these trains at any SNCF / DB (or just about every other country in Europe except UK for that matter..)' ticket counter. Booking from UK though as Jonathan says can be done through International Rail, or any other European rail booking agency sych as Rail Canterbury but they of course charge fees and mark-up..
If your in the southeast though and fancied a daytrip to Calais on the ferry from Dover you can of course book just about any European train there with those nice folks at la Gare de Ville! You travel free on P&O between Dover-Calais with your Priv / Staff travel card (its just a GBP1,50 port tax each way).
The alternative route (and indeed my favourite) from London to München is across Belgium and via Brussel and Köln. You book the Eurostar as normal (direct in person at STP is cheapest if your based in the SE), Then use your NMBS/SNCB and DB coupons from Brussel Zuid on any ICE/IC trains you like (no reservations are required on this route unless you wanted to use a Thalys train from Brussel to Köln or the Nightjet night train from Köln to München).
I can highly recommend the NJ night train down the Rhein from Köln, the couchette supplement with your DB coupon is about EUR30 and EUR54 in the sleeping car if memory serves. Both include breakfast and with the latter also a welcome drink of sparkling wine, goodie bag, bigger breakfast and shower access at the end of the car. I've done this off a mid-afternoon Eurostar from London, booked the NJ at the international ticket desk at Brussel Zuid before the ICE to Köln, enjoyed a moonlit run down the Rhein valley and been in München early next morning.
Have a great trip, its a fantastic city.
Happy FIP travels,
Kris