The duo, along with Pamela Relph, James Roe and cox Lily van den Broecke, saw off the challenge of Germany to ensure the last race of the Paralympics regatta at Eton Dorney finished with a GB success.
Marlow rowing club member Riches said: "I still can't believe it. It's just amazing to think we've actually done it.
"We've all worked so hard and now we've got the reward. It's just a dream."
"I've had amazing support. It's incredible how things like this brings people out. I had friends texting me telling me they've got tickets and I haven't spoken to them fro two or three years.
"I've been in touch with my closest friends from Marlow. They did an amazing thing for me, they gave me a little envelope that I had to open each day and they had fun photographs and quotes in there. They gave me all the support I needed."
She added: "It's been four years of blood sweat, tears but it's all been worth it. Crossing that finish line I honestly didn't know where we'd come. With my zero vision goggles on I was completely oblivious, I had to ask Pam where we'd come."
Ascot resident Smith said: "It's the proudest day of my life. This is the greatest thing that's ever happened to me.
"Thanks to everyone in Britain who has suported us."
Smith hailed the supporters who were packed into Dorney and said they helped get him and his crew mates over the line.
"When you hit that wall of noise it makes you dig that one per cent more," he said. "When we hit that noise today I was in so much pain but I managed to find that bit more.
"It was like every one of the crowd was taking every stroke with us today and I think that made a difference today."
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The Met Office has issued a yellow alert for Windsor and Maidenhead, Slough and Wokingham, warning that rain moving eastwards across the south of the country may turn to snow in some places.