2 option if you want to reach from Singapore to London by land.

Option 1

Route

If I start from Singapore (the tip of the Malayan peninsula), I will take a train to Butterworth in Malaysia followed by a train from Butterworth to Bangkok. From Bangkok, I will take a train to Udon Thani so that I can cross over to Vientiane (Laos) by Bus. From Vientiane, I will travel by bus to Hanoi then continue my train journey to Kunming and head straight to Beijing. From Beijing I will take a train to Urumqi in the Xinjiang province then follow it up with a weekend train ride into Almaty (Kazakhstan). I will then take another train from Almaty to Moscow, followed by Moscow to St. Petersburg and finally from St. Petersburg to Germany.

Time

I will give myself approximately two months. This includes rest in between the trips, and cater for technical and unexpected delays. I think there is a chance that it might take you a 1 1/2 months, but I highly advice against pushing it too short a time frame as immigration and customs might be nasty along some of the borders (i.e. bribes, long queues, etc.).

Costs

Inclusive of visas, food and rooms at hostels/guesthouses along the journey, I would set aside aboutUS$2,000 for the entire trip. Some immigration officials (especially along the Laos border) would request for a fee for immigration clearance, and that is taking into account as well for the amount I mentioned.

Option 2

Route

I have attempted to travel from Singapore to London overland, and in the end abort the trip when I reached Astana, Kazakhstan. My itinerary is as follows:

1. Singapore
2. Kuala Lumpur - via bus transfer from Aeroline
3. Butterworth - via train from KL
4. Hatyai - via cab and car transfer from Butterworth
5. Bangkok - via train from Hatyai
6. Aranyaprathet and Poipet (border town of Bangkok-Cambodia) - via car transfer
7. Siem Reap - via car transfer from Poipet
8. Phnom Penh - via car transfer from Siem Reap
9. Ho Chi Minh City - via bus
10. Hanoi - via train
11. Nanning - via train
12. Beijing - via train
13. Xi'an - via train
14. Urumqi - via train
15. Almaty - via train
16. Astana - via train

From Astana, you can book a train to Moscow, Saint Petersburg, and went on further to Europe.

Cost

From Singapore onwards, I would say set aside about USD5,000 to USD6,000 to be safe, depending on your preferences. I have land myself in several scams as I have no choice but to make the payment. Guess that's part and parcel of learning while travelling. Also, long-distance travel on train can be rather tiring and exhausting. So you might not even want to choose the cheapest alternative all the time. One issue with China trains is that if you are rushing, it is difficult for you to book the tickets that you want as well.

Time

I set aside two months to complete the whole journey. In the end, we took slightly more than one month to reach Astana. My take is two months might be a little too rush, given that you might not always go according to your plan. During this trip, I have cancelled several destinations due to inability to find the transport, and end up staying in one city longer than expected. Still, I think this is the beauty of a long distance trip like this.