This tab is almost identical to the one Tom plays on the guitar, but I'm certain 
it's not an Em on the part "In the river Thames".
But it was the closest match I could find.
Hope you'll get it right. It's very easy ;)
Enjoy!

Capo on 5th fret (You can put it on any fret you like to adjust it to your voice, 
but the original is on the 5th)

intro: C - G x2

What's up

G
I dreamed I was drowning

Em
In the river Thames

D
I dreamed I had nothing at all

C                       G
Nothing but my own skin


I dreamed I was drifting

Em
On the howling wind

D
I dreamed I had nothing at all

C                       G
Nothing but my own skin



Em                      A
Slipped away from your open hands

Fmaj7   C
Into river

Em                     A
Saw your face looking back at me

Fmaj7                          G
I saw my past, and I saw my future


G                            C
You take the pieces of the dreams that you have

                                 G
Cos you don't like the way they seem to be going

                                 C                          
You cut them up and spread them out on the floor

                             G
You're full of hope as you begin rearranging

                   F
Put it all back together

                         C
But any way you look at this

        G
Looks like

                 D
The lovers are losing



G
I dreamed I was watching

Em
The young lovers dance

D
I reached out to touch your hair

             C               G
But I was watching from a distance


Em                         A
We cling to love like a skidding car

Fmaj7         C
Clings to a corner

Em                   A
I try to hold on to what we are

Fmaj7                      C        G
The more I squeeze, the quicker we alter


G                            C
You take the pieces of the dreams that you have

                                  G
Cos you don't like the way they seem to be going

                                 C
You cut them up and spread them out on the floor

                              G
You're full of hope as you begin rearranging

                    F
Put it all back together

                         C
But any way you look at this

       G
Looks like
                  D
The lovers are losing


D (hold the chord all the way through this part) 
I dreamed I had nothing at all; Nothing but my own skin
(I dreamed I had nothing at all; Nothing but my own skin
I dreamed I had nothing at all; Nothing but my own skin)
I dreamed I had nothing at all; Nothing at all
D7

D7                           C
You take the pieces of the dreams that you have

                                 G
Cos you don't like the way they seem to be going

                                 C
You cut them up and spread them out on the floor

                             G
You're full of hope as you begin rearranging

                    F
Put it all back together

                         C
But any way you look at this
  
       G
Looks like

                  D    D7
The lovers are losing

D7                           C
You take the pieces of the dreams that you have

                                 G
Cos you don't like the way they seem to be going

                                 C
You cut them up and spread them out on the floor

                              G
You're full of hope as you begin rearranging

                     F
Put it all back together

                       C
But in the final reckoning

        G
Looks like

                  D
The lovers are losing




That's it! :)

Btw, let me know if you find the chord I could replace with that Em ;)