Hmmm.
I've just checked out Travel Unravel Holidays Private Limited on the Companies House website. It's a legitimate company, that's been in business since 2010, however all three directors have addresses in India, which is a red flag to me. (That's not racism. There are many excellent businesses run by people of Asian heritage but I do worry about how much time a director might have to spend on developing a company when he or she is based overseas).
Further, I start to worry when the directors of a company are also (or have been) the directors of lots of other similar companies. It suggests to me that they might be working to the principle (or should that be 'lack of principles') that if one company goes belly up, they can always fall back on the other for their income. For example, as well as being a director of Travel Unravel Holidays Private Limited, Sandeep Raj has also been a director of Holidays Dubai Ltd, Holidays Thailand Ltd, Airlines Flight Ltd, Cheap Flight Fare Ltd, AirwaysReservation Ltd, Airlines Reservation Private Ltd, AirlinesFares Ltd, TravellAll Ltd, AirwaysFare Ltd, CheapFlightDeal Ltd, Voyyag Ltd and Voyagg Ltd, all of which were dissolved within a year or two of being set up. (Those are just his UK appointments. He might well hold, or have held, countless directorships in other countries too).
So the answer to your question ("why are companies like this allowed to carry on trading?") is simply that they keep on trading until people come to realise that they're dodgy and then simply start all over again under another name.
I've never been a great fan of Skyscanner. It's a myth that they can always find the cheapest flights. Airlines hate such 'screen scraper' sites, as many airlines make much of their money from 'add ons' (such as accommodation, insurance or car hire) and thus need travellers to book through their own websites in order that they can then be offered such extras. They therefore do their absolute best to ensure that their flights aren't listed on Skyscanner.
Having said that though, I'm no great fan of the vast majority of High Street travel agent either. Most of their staff have virtually no training and rely solely upon what comes up on their computer screens, which isn't always the best information available. In my opinion, it's far better to do your own research or to get an amateur enthusiast (who can allocate hours to the task if needed, rather than the minute or two that a travel agent can) to do the searching for you.
If you'll provide the dates of your travel, together with an indication of where you'll be starting out from, I'll be happy to see what's available to you.