The Bella Bamba website reportedly received 19,000 hits within ten minutes of the collection going live, causing it to crash.
"Lots of my fans rushed to buy my bikinis as soon as the site went live," said Mecklenburgh.
"There was so much traffic it crashed! We've rectified everything as soon as possible so everything should be fine from now on.
"I can't believe we have had to order more pieces to be made because the demand has been so high - I'm so pleased they are proving so popular. I'm really proud of the collection."
The line features bikinis, monokinis, bandeau and strapless styles, and padded and classic strings, with crystal decoration.
Mecklenburgh also chose two fans - 19-year-old Kari Boanas and Jess Banks - to model the range with her.
"Bella Bamba is an exciting new brand to be part of and I can't wait to wear each style on my holidays this year!" she added.
"I'm really glad to have given two of my fans who represent real women a chance to model with me for the day. They were both amazing."
Bella Bamba directors Eleise Lucraft and Becky Majeed said: "Lucy was the perfect choice to collaborate with. She knows her fashion, is a beautiful girl who embraces her curves and loves to look good.
"Together, we have created a luxury collection of swimwear which not only looks sexy and stands out with sunlight-reflecting crystals, but the Brazilian cut to each piece ensures each style fits beautifully."
The collection is available now in sizes small to extra large (UK 8-16) with an RRP of £55 a piece.