I am considering buying a Fender 65 Super Reverb or Twin Reverb and my style is the same as Gregor Holden (gregsguitars). I am wondering whether or not a basic style drive pedal would suit for any other styles I play, ie crunchy British styles.

Anyone have any input?
It depends on the specific pedal, but yes. IMHO you can get in that ballpark even with a simple Tubescreamer-type pedal.

However, if that still doesn't satisfy you, there are Marshall-in-a-box pedals that give you a more British flavour -- and those Fender amps you're talking about take pedals really well, so that shouldn't be an issue. Go for it, man.
Squier "VMC" Stratocaster
PRS SE Singlecut
tc electronic polytune
CMAT MODS Signa Drive
Blakemore Effects Deus Ex Machina
DIY gaussmarkov Dr. Boogey
EHX Small Clone
Mooer ShimVerb
DIY Beavis Devolt
T-REX Fuel Tank Chameleon
Ampeg GVT52-112
Gilchrist custom
Yamaha SBG500
Randall RM100 & RM20
Marshall JTM45 clone
Marshall JCM900 4102 (modded)
Marshall 18W clone
Fender 5F1 Champ clone
Atomic Amplifire
Marshall 1960A
Boss GT-100

Cathbard Amplification
My band
personally I'd look at my amp choice again. maybe a more versatile amp would be a better option than a pedal. a 2 channel amp with good cleans and a nice overdrive section may be better for you.
Mesa Royal Atlantic. Superb american style cleans with amazing british flavored gain.

If a pedal is really what you want get a Catalinbread Dirty Little Secret.

Mesa Royal Atlantic
Emperor 4x12 Silver Bells
PRS Swamp Ash Limited Custom 24
EQD Acapulco Gold
MXR Carbon Copy
EHX Epitome
EHX Superego
Fuzz Hugger Algal Bloom
Way Huge Fat Sandwich
I love the tone I can get running my Fulldrive 2 into my old Fender. The OCD is another good option from Fulltone, but I don't have any personal experience with it. It seems to be more in the "distortion" realm of things while the Fulldrive is more of an overdrive, but turning up the gain knob on the Fulldrive gives you some great, natural sounding OD just from the pedal (especially when you run it at 18v).
Highway One Tele (w/Custom Shop 51 Nocaster pickups)
Standard Tele (modded to Nashville specs)
Reverend Roundhouse

Orange Rockerverb 50 MKI
Vox AC4c1
Jet City JCA20H

And pedals!

"Shiva opens her arms now..
...to make sure I don't get too far"