A few facts which contradict the proposal that construction of the Garden Bridge could begin anytime

The £100m construction contract with Bouygues was programmed to have been signed last September, but it remains unsigned because sufficient impediments remain to the delivery of the project, and the funding agreement from TfL precludes signing the construction contract until a number of key things have been achieved, including having secured all of the necessary capital funding. In October the Garden Bridge Trust told Lambeth that the contract needed to be signed off ‘within a few weeks’ or else they would have to re-run the tendering process. Two months later they have neither signed nor re-run the competition for the contract.
The Garden Bridge Trust have yet to even agree a first draft Heads of Terms for a variation of the lease from Lambeth Council (freeholder) and a sub-lease of the land for the bridge and Coin Street Community Builders (leaseholders). This agreement was also scheduled for sign off last September. If and when they do, the matter will then be held up for a further 6 months, since the site was recently designated as an Asset of Community Value which requires Lambeth to give a community interest group up to 6 months to come with an alternative offer for the site.
46 planning conditions were imposed by Lambeth, including one requiring agreement with ITV and IBM (adjacent landowners) on the use of their sites for construction access, and the mitigation of vibration from construction and noise from occupation of the Garden Bridge (there is some doubt as to whether ITV would even be able to use their studios during the 18 month construction period if the development goes ahead). Again, this was scheduled to be resolved by Oct 2015. (Incidentally, only 13 of the conditions have been discharged so far).

There is an as yet unfulfilled requirement by Westminster Council and Lambeth Council for the £3.5m annual operational costs to be guaranteed by an appropriate party, in case the Garden Bridge Trust are unable to raise these funds from galas, corporate events and t-shirt sales - which is the intention in their business plan. Last June, Boris Johnson agreed to provide such a guarantee by instructing the GLA and TfL to agree a mechanism to underwrite the operational costs, and the outcome of Michael Ball’s judicial review, was that they must reveal the contents of any guarantee to him (Michael), which has not happened. Lambeth have today confirmed that they still have not received the Operations and Maintenance Business Plan, which would include this 'guarantee’ issue, and would not expect it to be approved by councillors until July. This is a pre-commencement condition, so no construction can begin without it.
Although £20m of public funding has already been given to the Garden Bridge Trust (and around £9m spent on the design to July 15) the bulk of the money will not be released until all of the issues above are resolved. Given the timescales, it is almost certain that this money will not be released before Boris ceases to be mayor, and there must therefore be considerable uncertainty as to whether it will be granted with the new Mayor (one of the mayoral candidates has put down a motion at the GLA in the last few days demanding all public funding be withdrawn, and clearly the rows over procurement will make this more likely, particularly if Sadiq is elected).

The amount of private funding amassed is very opaque and looks increasingly unlikely to be as significant as claimed. The Trust claimed in summer 2014 that they have £65m of pledges and today, they claim £85m; so they have made little progress during the 18 months in which they should have got maximum publicity and raised the outstanding amount. We have big doubts about their claims: Glencore is one of their biggest donors and they are close to bankruptcy. With recent negative publicity, the GBT have been desperate to announce new money, but the best they could manage was a mere £5m pledge from Sky a couple of weeks back - and it quickly became clear this had been previously included in the total (which still remains at £85m). In short, their fundraising has not proved fruitful - but without evidence of all of the funding being in place, the remaining £40m of public funding will not be released, according to the terms of the funding agreement with TfL.
In conclusion it’s pretty obvious they are not going to be in any position to get on site and begin construction in the summer. They were initially intending to get on site last September; if they fail to get on by the summer they are almost certain to run into logistical problems with the construction of the Thames Tideway Tunnel. They always argued that this would force a 5 year delay, which would kill the project. But most engineering and logistic problems are resolvable, including this one, but the issue will then be considerable additional costs.