In a statement to the London Stock Exchange, it said: "The well is being drilled to an estimated target depth of circa 3,500 metres (11,480 feet).
"Drilling operations are expected to take approximately 30 days and a further announcement will be made once drilling is completed."
Mr Rammell told the House of Commons the government would take "whatever steps [were] necessary" to protect the islands and that it had made Argentina "aware of that".
Shadow defence secretary Liam Fox said "no amount of intimidation" from Buenos Aires could alter what was a "fundamental issue of self-determination".
Argentina has threatened to take "adequate measures" to stop British oil exploration in contested waters around the islands, and is seeking support from Latin American countries at a regional meeting in Mexico.
It wants its neighbours also to impose restrictions on shipping in the area.
Argentina can already count on support from President Hugo Chavez of Venezuela, who said Britain was being irrational and had to realise the "time for empires was over".
Nicaraguan President Daniel Ortega has called for "Britain to return the territory of the Malvinas to its real owners - to return it to Argentina" on Venezuelan Telesur television.
Argentina has long claimed the islands. It invaded the Falklands in 1982, before a UK taskforce seized back control in a short war that claimed the lives of 649 Argentine and 255 British service personnel.
But it has ruled out military action and is trying to pressure Britain into negotiations on sovereignty.
Last year Argentina submitted a claim to the United Nations for a vast expanse of ocean, based on research into the extent of the continental shelf, stretching to the Antarctic and including the island chains governed by the UK.
It is due to raise the issue at the UN later this week.
Desire Petroleum spokesman David Willie said: "Desire is an oil company and it's exploring for oil and not getting involved in what Argentina is saying about going to the UN. The rig is sitting firmly inside UK waters."
He added that Argentina was beginning its own oil exploration programme in the waters west of the islands.
Mr Willie said oil exploration in the Falklands was at an early stage, and even if commercially viable amounts were found it would be many years before the oil would start to flow.
The platform, the Ocean Guardian, has been towed 8,000 miles from the Cromarty Firth in Scotland.
Last week the Falklands Legislative Assembly, which sold the licence to explore for oil to Desire, said it had "every right" to develop "legitimate business" in hydrocarbons.
UK Foreign Secretary David Miliband said British oil exploration in the area was "completely in accordance with international law".
UK Prime Minister Gordon Brown also said the government had "made all the preparations that are necessary to make sure the Falkland islanders are properly protected".
DRILLING FOR OIL
The British oil rig has been towed from the North Sea, at a cost of $245,000 per day. It will drill wells in at least four of the offshore exploration areas known as "prospects"
In 1998 six wells were drilled, targeting one layer of sandstone - but not enough oil was found and the low price meant further exploration was abandoned
Now the price of oil has risen, there is potentially more profit to be made from drilling deeper, into untested sandstone on sides of basin
The area known as "Liz" will be the first prospect drilled - geologists say there is a 17% chance of finding an oil reserve of about 391m barrels
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.