If you put a phrase like 'send flowers abroad from uk' in a search engine you will see a page of results showing different companies that send flowers abroad. It's not easy to be sure of the cheapest because it will depend on the type of flowers - eg a bouquet of roses may cost more with one firm than another because one firm is including more flowers, or they are fresher or better arranged. You also have to be aware of hidden extras such as additional charges for same or next day delivery, so read the website information very carefully.
There are companies such as sendflowersabroad which specialise in doing exactly that, and they keep prices down as much as they can. If you look to the right hand site of their main page, you will see a list of the countries they send to and the prices.
On the other hand, if you want a company with a strong reputation that sends flowers to a large range of countries, you may want to look at a big international one like Interflora. Their prices compare well with most others and they are considered to be reliable.