I'm vaguely aware of the home guard and 'dads army' esque resistance...

In addition to the now well-known 'home guard', a typically less well-known element of the UK's post-invasion strategy concerns the 'Auxilary Units'. While the name may seem innocuous, their planned work would have been desperately perilous and likely to end in certain death in combat, or worse. The AU were drawn from the ordinary civilian population under utmost secrecy. They were trained as 'stay-behind' units of saboteurs and spies, who would have acted as the special forces under an anticipated British-government-in-exile.

To this day very little reliable information has been published concerning them and is still subject to the Official Secrets Act. Their existence was only disclosed in 1968, by historian David Lampe (The Last Ditch: Britain's Resistance Plans Against the Nazis), and were not allowed to parade at the Cenotaph on (British) memorial day until last year, by which point most of them were dead. Reasoning for their history being classified is that much of the planning concerning the AUs is likely to have been highly controversial. For example, AU members have since revealed that some of their duties would include murdering British individuals who would collaborate with the Axis occupying forces. Even more controversially, in the 'open in case of invasion' letters held by servicemen (ordered destroyed and unread when an Axis occupation was deemed unlikely), an ex-AU revealed in an interview that, of course, he had destroyed his letter, but "his friend" had opened his, which revealed that his immediate task was to murder the policeman who had interviewed him when he applied to join, in order to ensure the security of the AU.

Sources: John Warwicker (2005) 'With Britain in Mortal Danger: Britain's Most Secret Army of WWII'.

Further reading: 'Britain's WWII secret army uncovered' (BBC)

'Secret wartime resistance fighters are given an award' (BBC)

Several ex-AU have given (limited) accounts of their service, hosted on this website (which functioned as a source for Warwicker). Unfortunately many of these have 404'd. I will email them to let them know.

WW2; Winston Churchill`s Secret Army; The Auxiliary Units.. Pt1 (February 2013). A blog entry which condenses more information concerning the AU and includes links to other media, including video interviews. Especially vital is the 'Coleshill Auxilary Research Team', who have published material pertaining to the AU also, including the July 4th 1944 letter ordering a stand-down of the AU.

As far as scale goes, I think you have to include the Royal Navy and the RAF. These two forces were obstacles that had to be removed or neutralized for any cross-Channel invasion to have a chance at success. The Royal Navy dwarfed Germany's Kriegsmarine, and there was never a real chance at Germany winning or drawing a toe-to-toe slugging match in the Channel. British aircraft production outstripped German production during the Battle of Britain--a battle of attrition that consistently favored the British. Combined, these two forces were more than formidable. They could oppose any landing, then attack any forces that made it ashore.

I haven't studied the ground defenses to any real depth. The British Army lost a lot of its heavy equipment during the evacuation of Dunkirk, but they still had a good deal of manpower available. The process of reequipping the army obviously took some time, but every passing day meant that the army became more potent. That said, my favorite defense was the tiny Romney Hythe & Dymchurch light railway coastal armored defense train. The efficacy of a 15 inch gauge armored train is highly questionable. To me, though, it epitomizes the idea of 'British pluck.' In the end, the determination to use every available resource to resist the Germans may very well have been the most important aspect of British defenses.