During the band's incredible greatest hits set, guitarist pete townsend took a moment to pay tribute to Weller - who performed before the group took to the stage - and revealed the rocker had personally requested they play 'Pictures of Lily' for him in an email because it's his favourite Who song.
Townsend said: ''We were the mods, you were the mods, Paul Weller brought back interest in the mods and we're honoured to be playing with him. He requested this by email. We haven't played it for a few shows, so it'll probably be crap.''
Earlier, frontman Roger Daltrey mistakenly thought they were dedicating 'The Kids Are Alright' to Weller, saying: ''This song is for a special friend. We don't usually do requests, but for this man, Mr. Paul Weller, anything. It was him who asked us to play it.''
But Townshend interrupted his bandmate to say: ''I thought we were playing something else?'
To which a grinning Daltrey, 71, replied: ''I f***ed that up! I write these setlists the night before a show and always forget them. That time of my life when I forget everything is sitting on the doorstep.''
The band opened their show with 'I Can't Explain' and before launching into next track 'The Seeker' Townsend told the 65,000 fans in attendance: ''You are a long way away but we will f***ing reach you!''
Other highlights included 'Who Are You', 'I Can See For Miles', 'Pinball Wizard', 'Baba O'Riley' and 'My Generation', which prompted one excited fan in the crowd to light up a flare which was hastily taken off him by security.
Throughout the gig images of deceased band members drummer Keith Moon and bassist John Entwistle were shown on giant screens and before playing final song 'Won't Get Fooled Again' Townsend took a moment to remember his friends and praise their replacements, Pino Palladino on bass and Zak Starkey - who is Ringo Starr's son and former Oasis band member - on drums.
The 70-year-old musician said: ''Replacing John Entwistle was a hard job, as he had such a unique style. But this guy (Pino) is probably the best bass player in the world today.''
''You'll have seen pictures of Keith Moon on the big screen behind us tonight. When I see them behind me, I miss him terribly. But before Keith went, he gave this guy a drumkit, so in a way Zak studied at the feet of the w***er.''
After the band finished the playing the song, Townshend touched upon The Who's 50th anniversary, telling fans: ''We didn't think we'd last until the end of the week when we started. There was always a punch-up, we thought we'd split up every day. But then we lasted a year, and here we are. We wouldn't have made it without all of you. You've made it, without you it would not have happened.''
The group then departed the stage to huge cheers and the signature chant of ''we are the mods'', prompting Townshend to say: ''You're not mods, you're all too old to be mods. We are the sods.''
Earlier at the festival Weller treated the crowd to a run through of some his best loved songs, including 'Broken Stones' and 'You Do Something To Me', a handful of tracks from his latest album 'Saturns Pattern' and The Jam tunes 'Start!', 'A Town Called Malice' and 'That's Entertainment', on which he was joined by Miles Kane.
The Kaiser Chiefs performed before Weller and they were proceeded by Johnny Marr, whose set included The Smiths songs 'There Is A Light That Never Goes Out' and 'How Soon Is Now?' and a cover of The Clash hit 'I Fought the Law'.
Former Supergrass frontman Gaz Coombes opened the event.
A host of celebrities were at the festival, including Lionel Richie, ex-'Top Gear' presenter Jeremy Clarkson, Stereophonics singer Kelly Jones, retired England soccer player Ian Wright, TV host Fearne Cotton, actress Leslie Ash and her husband Lee Sharpe and comedian Rich Hall.
The Who now move on to Glastonbury and will close the festival on Sunday night (28.06.15).
The Who's setlist at Barclaycard presents British Summertime in Hyde Park:
'I Can't Explain'
'Who Are You'
'The Kids Are Alright'
'Pictures Of Lily'
'I Can See For Miles'
'Behind Blue Eyes'
'You Better You Bet'
'Love Reign O'er Me'
'See Me Feel Me/Listening To You'
'Won't Get Fooled Again'
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