We have a gmail address. We also have accommodation addresses in the UK and Australia but we have only had to use the UK one once.
We will shop by getting into the in country websites. We had a UK travel agent call us back when we were arranging a AI to Greece from the UK. We used my son's then address in London since they had to mail out the vouchers for some reason.
Once, when booking on a Europe site, we could not seem to get booked. Tried different credit cards. Finally, I realized that the on line form needed an EU address. I simply provided our address as the address of a hotel is Spain where we intended to stay prior...then the buy went through.
Some foreign sites want a local credit card. Our Visa and MC sometimes will not work but our Amex usually does. Some foreign on line sites do not seem to like premium credit cards either.
Booking our South African safari directly with the provider in SA was considerably less expensive than dealing with a local TA where we live. We communicated by email and on Skype.
We saved 30 plus percent over and above the quote from our US on line TA on a late booking Australian cruise simply by calling RCI in Australia. Their web site price was lower than their North American version. They knew we lived in Canada because of our customer number. No problem. My sister saved 15 percent plus simply by booking her Celebrity Baltic cruise through a UK travel agent.
Our custom is to arrange accommodation directly with the hotel, B&B, etc instead of using booking sites whenever possible. We typically either get a better price, a better room selection, or something additional thrown in such as breakfast.
When we went to Argentina two years ago I noticed the Aerolineas prices were better on their local site. I called the NA 1-800 number for Aerolineas and asked about these air fares. They gave me the number of the Buenos Aires call centre. I called, booked our internal flights, and saved 30 percent on the NA web site prices. They spoke english. They all seem to in the travel industry. Same for Turkey, but we were able to book directly on the web site for domestic flights. They were half of what expedia, etc were quoting for the same flights, same day, within 10 minutes of each other.
The prices are not always different than what we see on NA web sites however our experience is that it pays to shop. We are retired, so working the keyboard for a few hours can pay dividends. I guess you might call it the grey market for travel products. Not very grey though because the world has become a much smaller place from many perspectives. Naturally, we only use currency adjusted pricing for comparisons.