Environmental campaigners have warned the news is “unprecedented” and that global warming poses a “grave threat” to rivers.
Forecasters are continuing to warn of hotter temperatures to come, with a further blast of 30C heat predicted for next week.
The Thames has shifted from its official start point in Kemble, outside Cirencester, Gloucestershire, during the dry weather and is now more than 5 miles (8km) downstream.
Dr Rob Collins, science director at the Rivers Trust, told the Guardian: “Following prolonged dry weather, the source of the Thames in Gloucestershire has dried up, with a weak flow now only just about discernible more than 5 miles downstream (at Somerford Keynes).
“Under our changing climate we can anticipate the frequency and severity of such periods of drought and water scarcity to intensify, with increasing competition for a dwindling resource and devastating impacts on aquatic life.”
While Christine Colvin, advocacy director at the charity, added: "What we’re seeing at the source of the iconic River Thames is sadly emblematic of the situation we’re facing across the country, now and in the future.
“Whilst it’s not uncommon for the source to be dry in the summer, to only be seeing the river flowing five miles downstream is unprecedented.
“The climate crisis is leading, and will lead, to more extreme weather including droughts and heatwaves. This poses a grave threat to rivers and, as a result, the wider landscape.”
She continued: “We’re going to need to act at all levels to build resilience against this inevitable future.
“This means detecting household leaks, fixing mains infrastructure leaks, more efficient water use domestically plus implementing sustainable drainage solutions as part of desperately needed green infrastructure."
Met Office experts have said little rain is expected in the next week, while temperatures will remain cooler than in previous weeks, but could still reach the mid-30s.
“Many areas of the UK, especially the south, will witness temperatures several degrees higher than average, but these values are likely to be well below the record-breaking temperatures we saw in mid-July,” chief forecaster Steve Willington said.
“As the high pressure builds there is very little meaningful rain in the forecast, especially in those areas in the south of England, which experienced very dry conditions last month.”
While areas including Kent and Sussex are now experiencing restrictions on water use.
Mark Lloyd, Rivers Trust chief executive, told the Times: “Every year we get to this perilous position and at the last possible moment, when the rivers are at their lowest, we get discussion of temporary use bans.
“Announcing it at the last minute causes people to rush to wash their cars and fill paddling pools, and causes an increase in demand.
“This should happen before the rivers come to a desperate condition and there’s not enough water for wildlife.”