You need to book Eurostar to Paris ASAP. There is not much availability left for next week (limited quota, can sell out weeks in advance) -> 30€ seat reservation

Check here : https://www.b-europe.com/EN/Booking/Pass#TravelWish

Transfer in Paris : easy by metro (not included)

TGV Paris - Milan 30€ seat reservation, cheaper going to Bellegarde, then Geneva and Milan

Milano Porta Garibaldi - Centrale : walk or subway

There is a limited number of pass holder seats on the Eurostar between London and mainland Europe. On popular departures and during high season those sell out weeks, and sometimes months in advance.

The best place to see the availability of passholder seats and make reservations on the Eurostar is 

https://www.b-europe.com/EN/Booking/Pass#TravelWish

If you don't get any result, press "later trains" and eventually you will find the next available connection. 

If you have a mobile pass you need to generate a Pass Cover Number in order to make the reservation at b-europe. You do that here in the PCN generator:

https://community.eurail.com/news-and-announcements-39/pass-cover-number-generator-is-live-5653

Btw for next week you need to book high-speed trains ASAP. There is a holiday weekend and a lot of trains may already be sold out

Let us know your travel date for more precise advice

If London - Paris is unavailable, try London - Lille (or London - Brussels) using my link but you won't be able to make it to Modena in a day.

Paris - Milan can also be done via Strasbourg and you don't have to cross Paris and Milan by subway : leaving London at 06:01 (07:01 might be possible but 30-35 min is a bit short for transfer to Paris-Est) and arriving in Modena at 21:19. Costs : 30 + 10-20 + 13 = 53-63€

Using the direct train TGV Paris - Milan : 30 + about 30 = 60€. You need to leave London at 7 or 8am and you won't arrive until 10-11pm as the 15 min connection between Milano Porta Garibaldi and Centrale is not possible

I guess you'd like to travel in one day ?