Is the "Young Driver Surcharge" fee the same for all car rental companies in the UK?

No, these fees may vary, as may the age range they are applied for. Note also these change significantly between countries (and in some cases even between locations within a country).

Some of the main supplier's conditions in the UK:

Supplier   MinAge   Fee   NoFeeAge

Alamo        22     £27^     25
Avis         21     £45      25
Budget       23     £39"     25
Enterprise   25      ?       25°
Europcar     22     £31      25
Hertz        23     £31"     25
National     22     £27^     25
Sixt         21     £36      25*
Thrifty      21     £25"     25

"incl. tax - suppliers with no note may or may not be incl. tax

^excl. tax - suppliers with no note may or may not be incl. tax

°Enterprise is not very clear; the selection form allows selecting age 18-24, but the terms say minimum age 25. Also the selection form returns an error saying 'some locations' may have age restrictions on all UK locations I have checked.

*Sixt is not consistent in what is says on it's site. The Rental Guide says ages 21-23 will face the charge and mentions neither car classes on the amount payable, the Rental Information says all drivers below 25 pay £36 and lists a range of car classes which basically comprises all available for hire below the age of 25.

One additional note for the northern regions: Arnold Clark rents cars without young driver surcharges in some locations - T&C.

Here are links to the relevant pages of the mentioned suppliers - with the exception of Avis which does not allow direct linking to any useful page it seems: Alamo Budget, Europcar, Hertz, National, Thrifty