I'm not sure that's right, the Romans introduced lots of new foods to Britain but I've never heard of rice being one of them. The Italians didn't start growing rice as far north as the Po Valley (where risotto rice comes from) until the 15th century.
You might be thinking of the Roman Warm Period, during which Europe was slightly warmer, but this, like the Little Ice Age of the medieval and post-medieval periods, was just a localised deviation in temperatures. It wasn't a global increase in temperature, so didn't cause the problems that current global warming does or will.
In his book
The End of Roman Britain, Michael Jones has a chapter on the changing climate of fifth-century Britain. Tacitus writes in
Agricola that the soil in Britain is fertile and that crops grow quickly there, but also that they ripen slowly because of the heavy rainfall and dampness of the soil. During the Roman era, the climate in Britain generally was favorable for agriculture, although much of the land, especially in the highlands, was only marginally so.
From the second through the fourth centuries, the population of Roman Britain has been estimated to be approximately 3.5 million people. Jones contends that feeding this number would have put considerable strain on the ecology. Fifty or sixty thousand cultivated acres, alone, would have been required to feed the approximately 50,000 soldiers stationed in Britain in the first century AD. There were other environmental demands, as well, including fodder for military animals and quantities of iron, wood, and leather for construction, roads, and tents.
The native Britons would have been hard pressed to pay the cost of sustaining such a presence. A growing population, urbanization, and the demands of the Roman army and government would all have intensified agriculture and grazing in previously undeveloped areas. In time, he argues, this over-utilization of the land would prove to be disastrous.
Rice was known to European people as early as in the Roman period, when rice was also used as a medicinal herb.