中文都叫拒签，英文却有区别：rejected or refused. 意思可是大不一样！
从你的叙述看来，你当初的情况是rejected(即不受理，因为你的application是invalid), 而不是refused(拒签）.
Sections 3C of the Immigration Act 1971给in-time applicant赋予了临时合法居留权，来覆盖如果HO在签证到期后才给出签证的那段时间。所以，你的那段时间属合法居留。
现在HO拒你（这次的应该是refused, 因为给了你上诉权，这是对你valid application做出的decision), 可能是你自己胡填干扰了HO的判断。
上诉吧，能赢得。把3C的出处说明一下，说明那次不存在非法居留的问题。再说明一下这次申请时你一时糊涂把上次错看成非法居留给填上了。
没有找到Immigration Act 1971, 下面的连接是十年永居申请文件有关合法居留的说法。法律来源相同。
http://www.ukba.homeoffice.gov.uk/sitecontent/documents/policyandlaw/IDIs/idischapter18/longresidence/Long_Residence_IDI-_final_d1.pdf?view=Binary
Sections 3C and 3D of the Immigration Act 1971 both extend individuals’ leave in certain circumstances.
To prevent applicants from becoming overstayers through no fault of their own, section 118 of the Nationality, Immigration and Asylum Act 2002 introduced an amended Section 3C into the Immigration Act 1971.
Section 3C extends leave where a person with leave to enter or remain makes an in-time application (i.e. an application made before their leave expires), but where leave expires before a decision on that application is reached. Where a person has 3C leave, and his/her application is refused, 3C leave continues until appeal rights are exhausted. Section 3C only applies to in time applications. If a person submits an out of time application, they will have a gap in continuous lawful residence from the date their leave expired until the date that they are next granted leave, regardless of how long it takes for the decision to be made (see Example 5).
To prevent people becoming overstayers while exercising a right of appeal against a decision to curtail or revoke leave to enter or remain, section 11 of the Immigration, Asylum and Nationality Act 2006 added section 3D to the Immigration Act 1971. When leave to enter or remain is curtailed or revoked, Section 3D extends it while an appeal is brought and while it is pending and continues until appeal rights are exhausted.
