The lengthy process can be accelerated by simply removing the water present in the starting material, the University College London team discovered.
Following such shrinkage by a factor of at least 100, tissues could be created in 35 minutes.
This speed may one day allow doctors to make tissue implants at the bedside, Advanced Functional Materials reports.
Currently, scientists make tissues to be used for operations such as skin grafts by building a scaffold of cells that grow in the lab.
However, it can take between one and 12 weeks to grow enough of the required tissue for the surgery.
Professor Robert Brown and colleagues investigated whether they could cut this time down.
They experimented on making a tissue called collagen, which acts as a structural support for skin, bones and tendons.
Spare parts fast
Sucking out the water using a technique called plastic compression meant they could make the collagen in just over half an hour.
The tissue was not only made much faster than that made in the conventional tissue engineering way, it also appeared to be stronger, more like real collagen.
Professor Brown said: "Our method offers a simple and controllable means of quickly engineering tissue structures.
"The next stage is to test whether this method could help repair injured tissues.
"Ultimately, the goal is to design a rapid, inexpensive, automatic process for creating strong tissues which could supply hospital surgical units with a tool kit of spare parts for reconstructive surgery.
"The speed and control it offers means that our method could one day be used to produce implant tissue at the bedside or in the operating theatre."
Professor Tim Hardingham, from the UK Centre for Tissue Engineering, said: "The method has great potential for further development in clinical applications of tissue repair where immediate mechanical strength is required.
"Its success in these applications will depend on how it is survives in the body and how it is remodelled by natural body processes.
"It also needs to be known whether it can act as a template that is replaced by normal functional tissue. The present work provides a good experimental basis for these further studies."