In the early Nineties, Venezuela was a leading backpacker destination. Then the national airline suddenly collapsed. Viasa was a dreadful airline, but goodness it was cheap. I was one of thousands of travellers taken by Viasa to various corners of Latin America; plenty of us took the chance to stop off in Caracas to discover superb Caribbean beaches, vast landscapes and hidden colonial cities. Overnight, Venezuela was erased from the travel map.

Incredibly, the latest candidate for obscurity is India. If you have visited the Aldwych in central London recently, you will have seen why. When prospective visitors spend longer shivering in a queue to be sure of a visa than they do on the plane to India, something has gone badly wrong.

India can reasonably claim to be the most alluring nation on earth – not just for the colours, flavours and landscapes, but for the one-billion-plus people, many of whom seem to share the same trains as me. The new film The Darjeeling Limited misrepresents life aboard the world's finest transport undertaking, Indian Railways. (On pages six to nine, Michael Wood better conveys the convivial reality of Indian trains.) But unless the red tape gets untangled, these could be the last days of the Taj for disappointed British travellers who forsake the chance to see Shah Jahan's monument to love in Agra.

The half-moon-shaped Aldwych is the most international location in the capital. Much of it is occupied by BBC World Service, probably the most effective "travel advice" service in the world: if you want know the state of the transport system in flood-ravaged Bangladesh, or the advisability of crossing certain frontiers in Africa, the 24-hour news bulletins of World Service could well provide the answer.

The eastern end of the Aldwych is occupied by Australia House. The High Commission receives far fewer visitors these days, thanks to the enlightened introduction of the "electronic travel authority" scheme to replace the red tape of tourist visas.

At the eastern end of the semi-circle, and at the bottom of the bureaucratic food chain, stands the Indian High Commission. Prospective visitors to the most populous Commonwealth country have long been used to a choice: either apply for a tourist visa by post, which takes a couple of weeks, or turn up in person at around 8.30am when the doors of the visa department open. After a couple of hours chatting to fellow tourists and Britons of Indian descent, some unchallenging form-filling and a bit of queuing, a tourist visa was smartly stamped in your passport.

Yet this cheerful corner of the world has acquired the characteristics of a refugee camp, populated by hapless individuals enduring discomfort and despair. In the summer, the government in Delhi abolished the issuing of visas by post. Initially, tourists were not too badly affected; but once autumn began, the queues began to grow.

The visa-by-post scheme was brought back at the start of November, but by then the backlog was running into thousands. By Monday morning 12 days ago, tourism to India had hit the bureaucratic buffers in London WC2. The queue stretched for most of the 180-degree arc around the Aldwych. At 6.30am, I counted 163 people waiting for permission to visit the jewel in the crown of Asian tourism. By the time the doors opened two hours later, several hundred more had joined them – including some, towards the back of the queue, with pressing personal reasons for needing that precious permit.

"I'm going to a funeral in two days' time," one harrowed applicant told an official.

"The only thing you can do is come back early tomorrow morning," the official said. "It's first come, first served."

At the head of the queue was Jordan Mellor from Newcastle, who had turned up over 10 hours early. "I've got a load of money I want to spend. The longer I stay in England, the less I'll have. I am in the first 10 in the queue, which means that by 11am I'll have a visa."

An Estonian courier from a visa agency had joined the queue at 4.30am to make sure important business clients got their visas, and said it brought back unhappy memories of the Soviet Union, when it was said that the rouble was "a piece of paper giving us the right to stand in line and be humiliated".

About 10 miles away, in the exotic east of London, the Incredible India stand dominated the World Travel Market trade fair. While tens of thousands of pounds were spent on enticing capricious tour operators, hundreds of increasingly frustrated travellers were vowing to go somewhere less complicated next time.

Could Leena Nandam, joint secretary at the Ministry of Tourism in Delhi, offer any hope for visitors? "In the next two weeks this hurdle is no longer going to exist." Perhaps you would like to check this out on Monday morning. In the longer term, life could become easier.

"We are trying to take this to the next level, in the form of 'visa on arrival'." This system is used successfully by nations like Egypt and Kenya, which claim a £20 or £30 admission fee from every visitor. The tourist is happy to avoid the bureaucracy, and also to travel at the drop of a turban. But Ms Nandam would not be drawn on a timescale.

Meanwhile, Malcolm Louzado, the unfortunate man at the end of the queue, was booked to go to Goa in five days' time. "I'll get here at 5am tomorrow," he said. "At least it gives a taste of the disorganisation I'm going to face when I get there."