After the latest incident, the theft of Galanthus Mighty Atom, Wisley curator Matthew Pottage tweeted: "Goodbye named snowdrops. More plant theft at RHS Wisley. Just appalling. If you visit us, please help by being vigilant."
He said: "It is very upsetting for the team who treasure our collections. We will be stepping up measures to stop this unsavoury activity and we will not let it dilute the excellent diversity of the plant collections at RHS Garden Wisley."
Pottage told Horticulture Week: "The theft of plants at Wisley has increased in frequency over the past three years to around 10-15 plants a year. The thefts have included woody and alpine plants, perennials and bulbs, and have focused on some of the more unusual cultivars. We report all thefts to the police and are vigorously looking at ways to combat what can be a damaging problem for some of the more specialist cultivars."
The RHS said it does not know why thefts are rising but visitor number increases could be to blame, with 1.087 million visiting the Surrey garden in 2015, up six per cent on the previous year.
Twitter user David Morris wryly suggested "wiring plants to the mains" to deter thieves, while Wisley gardener Brendan Arundel called the thefts "utterly disgraceful". Gardening group All Horts tweeted: "Pretty miserable. Sorry to see that happen when the gardens give such joy to so many."
Also on Twitter, gardener Kerry Austen said: "Disgusting. Some people have no morals." Garden fan Robert Webber said: "So sad. Expect plant lovers to be different, but sadly still same cross-section of society." Gardener Rocky Coles said the theft "cues airport-style security scanners at entrances/exits".
In January 2014 the smallest water lily in the world, the endangered Nymphaea thermarum, was stolen from the Princess of Wales glasshouse at Royal Botanic Gardens, Kew.
Bulbs of new snowdrop varieties can be worth up to £100 each. Some gardens such as Harold Hillier Garden in Hampshire keep snowdrops locked away and on limited display.
Taking any wild plant without the landowner's permission is considered an offence under the Wildlife & Countryside Act 1981, though there are concerns that it is rarely enacted. It is illegal to take any plant growing in council parks or on council-maintained displays, such as roundabouts, without permission
While it is illegal to damage or disturb the habitats of protected animals, there is currently no offence for reckless destruction of the place where a protected plant or fungus grows. Non-commercial gathering of fruit, nuts and plant leaves is not normally considered an offence.
A Kew spokesperson said: "We do have occasional plant theft from our collections and we regard any theft as a serious matter. We have recently put in place additional electronic surveillance to augment the existing coverage."
Royal Botanic Garden Edinburgh curator of living collections David Knott said: "My key message is that we are cultivating plants for wider public enjoyment and removing pieces does detract and spoil it for others. With many plants we grow there are conservation messages with them so taking plant material doesn't send the best message."
He said: "It's certainly a sign of the times that we had to install CCTV when we built the new alpine glasshouse [in 2013] - CCTV was a key element of the specification.
"We have had specific instances of plants being stolen. People know exactly what they're stealing. They are knowledgeable. They are undoubtedly collectors which is quite disappointing, sad, frustrating and annoying."
He added as well as CCTV: "There's probably an education message out there. The analogy I use is with theft of bird's eggs, because of their rarity. Plants are there to be enjoyed by a wide cross-section of visitors.
"We have theft on a similar scale to Wisley. As a public botanic garden with open access we have a huge degree of trust and people are quite clever. They know how to take a tiny but and unless you know your plant collection it's easy to disguise so it's not immediately obvious."
He added: "Snowdrops are an obvious target when in flower and then as the best material becomes available for propagation. With the scale of our plant collection [273,000 individual plants at RBGE and its three satellite gardens] we can't monitor constantly."