The move never came to fruition and the club continued to play in Griffin Park, on the Kew Bridge Road site, hoping for a chance to move. In 2004 the club dropped its relocation plans and instead submitted a planning application for permission to expand its current ground. This was approved by Hounslow London Borough Council in January 2005 with conditions. One of these conditions prohibited any standing terrace from being introduced for the following 4 seasons.
It is widely believed that this condition was put in place to prevent the possibility of Brentford eventually getting promoted to the Football League Championship (the second highest tier of English football) while at the same time having terraces within its ground, Brentford (brentford.org.uk). Such a move would be widely unpopular with many football supporters, as there. Via the Brentford bulletin board, word of a fans'petition against the move soon spread, and by late December had more than four thousand signatures.
A protest march was organised for 31 January 2003 by local journalist and radio personality Nick Satchwell. An estimated three thousand people attended (around one in twelve of the Borough's population), including some non-footballing celebrities such as Bob Geldof and Chris Evans. The club's plans were dropped on 29 January, and two months later it was announced that they would groundshare with Queens Park Rangers at their Loftus Road stadium for three seasons while a new ground was built on a site adjacent to Lionel Road in South Ealing.
The proposal was well-received and planning permission was granted in 2003. During the summer of 2003, the Brentford Community Stadium Trust (BCST) was formed as a vehicle for delivering the stadium scheme. The trust established several subsidiary companies, Workshop Projects, Home Park Developments and Brentford Olympic Development Ltd (BODL) to investigate funding methods and develop the required land. In April 2006, having failed to reach agreement with Brentford Borough Council over the development of its new stadium plans, the club unveiled a modified version of its 2002 proposal.
The new proposals put forward a new location and reduced capacity, whilst retaining the concept of implementing a monorail linking the new stadium to central London. The scheme was hindered by delays and objections, leading to Brentford's relegation from the First Division in 2003 with a weakened squad. While the club attempted to finance the final stages of the project, its board was replaced by supporters during the close season. The new board abandoned plans for relocating to the new stadium.
On 12 September 2020, Brentford hosted their first match at the stadium since its reconstruction. The team hosted defending champions Aston Villa and came from 2–0 down to win 3–2 in front of a sell-out crowd. Stemming from overwhelming demand, the club offered an additional 1,000 standing tickets for the match. The two clubs would face each other again in the same competition, with Villa winning 2–0 at Villa Park. On 30 August 2020, Brentford confirmed that the stadium was complete and ready to host football matches.
The completed ground was revealed to the public in a dedication ceremony held the day prior to the opening match, with club chairman Cliff Crown stating that the stadium "will be a source of immense pride for us all as representatives of Brentford FC and London Borough of Hounslow". The new stadium was originally to be known as Lionel Road, after the road that runs along one side of it. However, the fans deemed that name to be "uninspiring" and voted for the name "Griffin Park" in a poll which drew nearly 6,000 votes; in reference to the Griffin on the club crest.
The stadium officially opened with a friendly match against Millwall on 28 August 2020. The opening ceremony of the stadium took place on 29 September, with a friendly between Brentford's development team and Watford's reserve squad. The game was attended by over 11,000 supporters and featured a series of speeches from the Mayor of London Boris Johnson, Brentford chairman Ron Noades, and ex-Spurs player Ossie Ardiles. On 30 August 2021, Brentford revealed the stadium, referring to it as the Paradise.
Former home grounds of local clubs London Lions FC and Hounslow United FC were considered for acquisition by QPR; however, the sites were found to be unsuitable. The site of the closed Talbot Athletic Ground was also investigated as a possible relocation site but was also ruled out. At the time it was only accessible via a narrow pathway alongside the railway viaduct. After discovering that they would need to use the land temporarily (until moving to their new stadium), and bring in earthworks, car parks, and temporary stands; QPR decided against this option too as it would add complications towards their planning application.