How to get casting professionals to take you seriously if you live outside London

If you live outside London you should not necessarily view this as a negative aspect. Instead you must focus on the positive always in this industry and use that to market yourself. This maybe that you have an interesting accent that allows you to stand out, or even better if you can perform in your regional accent and also have the ability to speak using a London accent - if so, high light this in your covering letter and if not it will not hurt to learn a standard London accent. If you are willing to travel to London and if you have a base (place to stay in London) clearly state this also. Remember even though London is the capital of the UK and the major auditions may take place here, it is becoming more common for drama series to be filmed outside of London - for example Skins (Bristol) and Waterloo Road (Scotland).
Also be aware that the majority of casting directors who cast for the main television shows for ITV and BBC are based in the north of the country (Manchester)!.
It may be a good idea to start with a good agent who is based in the area you reside, who has the contacts with industry professionals in London, if you perform a successful audition and secure a credible agent, that in it's self will encourage professionals within London to take you seriously.
You also will benefit yourself by studying an accredited Actor course at a reputable Drama School, investing in quality headshots, registering with Equity, and joining websites should as Casting Call Pro and Spotlight.
It is unlikely that a casting director will dismiss an acting submission on the basis that they live outside of London, if you have the "look" for the character they are casting for, good credits and a showreel that demonstrates your versatility as an actor, you increase your chances of being offered an audition slot. Following this stage you may get a offered a role, if those casting view you talent as an actor (along with your attitude/ appearance) as of better value to the script, cast and crew than the other auditioning at that particular time. If the casting director/ director and sometimes writer are wowed by you it has been known for some companies to provide you suitable accommodation for the duration of your filming, if you do not reside in London.