We start with the Intro, starting and ending with the root note (G):
G7
E|---------------------------------------------------| I
B|---------------------------------------------------| I
G|----3---3b-5-3-5b(7)-5-3-5-3-----------------------| I
D|-/5---5----------------------5-3-5-5---3---3-5-5---| I
A|-------------------------------------5---5---------| I
E|---------------------------------------------------| I
0:00

D7
E|---------------------------------------------------| I
B|---------------------------------------------------| I
G|---------------------------------------------------| I
D|----3---3b-5-3-5b(7)-5-3-5-3-----------------------| I
A|-/5---5----------------------5-3-5-5---3---3-5-5---| I
E|-------------------------------------5---5---------| I
0:04

G7
E|---------------------------------------------------| I
B|---------------------------------------------------| I
G|----3---3b-5-3-5b(7)-5-3-5-3-----------------------| I
D|-/5---5----------------------5-3-5-5---3---3-5-5---| I
A|-------------------------------------5---5---------| I
E|---------------------------------------------------| I
0:10

E|-------------------------------------------------------------------------|

Now let's have a look at some essential licks from the Blues Breakers version. Look at 
lime-line to locate
them. You need some more fingering patterns from the G Blues scale now.

G
E|------------------------------------8b(10)-6b--6b(8)rb6--3---3-5b(7)-3-5------------------| I
B|--------------------------------/8~~-----------------------5--------------------3---3b----| I
G|---3-/7~~--7\--5-3-5-3-----3b--------------------------------------------(7)rb5---5----5--| I
D|-5---------------------5-5----------------------------------------------------------------| I
A|------------------------------------------------------------------------------------------| I
E|------------------------------------------------------------------------------------------| I
0:15                             0:19                                         0:27

G
E|-----------------3---------------------------------------------------------------------| I
B|-------3-------3--------------------------------6-6------------------------------------| I
G|-5b(7)---5b(7)-----5b(7)rb5-p3---5-3---------/7-7-7---(7)rb5-3-5-5---5-3---------------| I
D|-------------------------------5-----5-3-5-------------------------5-----5-3-5---...---| I
A|---------------------------------------------------------------------------------------| I
E|---------------------------------------------------------------------------------------| I
                 0:29                         0:33

Another good lick, often repeated, is at 00:40:
E|--------------------------------------------------| I
B|----13b(15)rb13-11-13----11-13b(15)-11b----11\----| I
G|----------------------12----------------12--------| I
D|--------------------------------------------------| I
A|--------------------------------------------------| I
E|--------------------------------------------------| I

E|-------------------------------------------------------------------------|

Rhythm guitar during organ solo at 01:02 (still Blues form!)

     G7       C7       D7
E|-------------------------------| I
B|-------------------------------| I
G|----------------5-3-----7-5----| I
D|------5-3----------------------| I
A|--------------3-------5--------| I
E|----3--------------------------| I

E|-------------------------------------------------------------------------|

After the organ solo some nice bendings:

E|--------------------------------------------------------------------------------------------| I
B|------6h8~~---11b(12)--13b(15)-13-11-13-11~~--12b-12-13-12-13-12br----------11-14b-11b~~----| I
G|-/7~~----------s| low------------------------------------------------12~~--12-----------------|I
D|--------------------------------------------------------------------------------------------| I
A|--------------------------------------------------------------------------------------------| I
E|--------------------------------------------------------------------------------------------| I
01:19                   01:23                                       01:28

E|-----13---------------------------------15------15------------------------------------------| I
B|-13b----rb13-11-13----11b(13)----11-----18b(20)----18-15-18b(20)-18-15----------------------| I
G|-------------------12---------12---------------------------------------17b(19)-17-15----17--| I
D|-------------------------------------------------------------------------------------17-----| I
A|--------------------------------------------------------------------------------------------| I
E|--------------------------------------------------------------------------------------------| I
                              01:32                                     01:35

E|------------------------------------------------------------------------| I
B|----------------15-------------so| und like-------------------------------|I
G|-----15-17(b)19----17p15----17-a| break here---(18)rb17-15-------15b-----|I
D|--17---------------------17-------------------------------17-17---------| I
A|------------------------------------------------------------------------| I
E|------------------------------------------------------------------------| I
                                01:37

E|-------------------------------------------------------------------------|_

Finally the end of the end:
E|---7\-7\-7\-7\-7\--4\---0---0-----------------------------0-----| I
B|---6\-6\-6\-6\-6\--3\---0---0-----------------------------0-----| I
G|---7\-7\-7\-7\-7\--4\-----------7b(9)~~--7--4-------------------| I
D|----------------------------------------------7-5---------------| I
A|-----| not sure about...----------------------------5~~-----------|I
E|--------------------------0----------------------------0--------| I